Simply, put, no. Searle in this article is approaching the analytic-synthetic difference by showing the role of metaphysical presupposition in evaluating a statement.
Pages 166 and 167 have everything right there, but admittedly, it's very dense and it helps to have some background information on the a priori and a posteriori, the analytic-synthetic distinction, the notion of Sinn und Bedetung, and the descriptivist theory of names as well as alternative theories of names.
It is Searle's contention that both a) and b) are not fundamentally different in the absence of metaphysical presupposition; he seeks to show that even a statement like 'a=a' is contingently true. From p.167:
(a) and (b) above... are analytic...
This, of course, is what you're asking. Why isn't it b) synthetic? He gives an example that shows that context is important for determining whether or not the Law of Identity holds:
[T]hat the same mark refers to the same object on two different occasions of its use is a convenient, but contingent usage.
Thus, the traditional criterion of deciding if the subject is somehow inherent in the predication is merely a metaphysical presumption. That is to say, it's not even necessarily true that in the proposition 'a=a', the first and the second 'a' refer to the same object or if you prefer, possess the same reference. He goes to give an example from cryptography:
Suppose the first time an object is referred to in our discourse it is referred to by 'x', the second time by 'y', etc. For anyone who knows this code 'x=y' is trivially analytic, but 'x=x' is senseless.
What does this mean in simpler words? The relation of the symbol 'x' to 'y' is relative to how the tokens and to what they refer are used in the language-game! What Wittgenstein grasped in his Philosophical Investigations was that symbols used in language are inherently normative, and where there is public language and shared meaning, there is ultimately convention. Elsewhere he speaks to how the Law of Identity in the use of proper names can be used synthetically:
[I]ndeed, some identity statements using two proper names are clearly synthetic: people who argue that Shakespeare was Bacon are not advancing a thesis about language.
Hence, the criterion for determining the analytic and synthetic nature of a proposition is not captured in the tokens proper, but rather is a function of the conventions of the language game.
An example will suffice to clarify: Let's invent a language-game. We translate tokens to descriptions. The truth of the proposition is determined by the biconditional function. (This is a very simple use of synonymy to establish identity.)
Rule 1. The first time a string token is used to refer to the historical entity known as Marcus Tullius Cicero, first 'Marcus' must be used, the second time 'Tully', and the last 'Cicero'. For subsequent invocations, just repeat in the spirit of the modulo operation.
Rule 2. Any reference to a fictional entity, such as in a mention in a work of Shakespeare, who is roughly based on Marcus Tullius Cicero must be referred to by 'Tully'.
Now, this is NOT a conventional way to use proper names. It inherently causes confusion, but Searle's point is simple. That "'Tully=Tully' is analytic" is contingent, not necessary. The reasons for the convention are intuitive, but it unnecessary to explain. Now, examine the short passage.
"Given the historical accuracy of the passage, the historical Marcus is Tully in the work of fiction; Tully is Tully."
Now, in the second sentence, 'Tully is Tully' is actually synthetic despite the fact that the tokens are identical! That's because they refer to two different things. That is, if one only uses the criterion to determine whether a sentence contains the same token being used, it appears analytical. Yet, in the context of the passage, the meaning is an elliptical construction read as "(Thus, the historical) Tully is (the same as the fictional) Tully (in this regard). Clearly they don't have the same reference and therefore don't obey the Law of Identity in this application of natural language.
Even more importantly, how do we know in this language-game the same cited proposition "Tully is Tully" is true or not? Because we have empirical evidence, in this case, of the historical accuracy of the fictional passage to decide. Thus, our reliance on that evidence makes the proposition synthetic.
So, to address your own example, it is not appropriate to draw the following conclusion without appropriate qualification:
(a) "Tully = Tully" is analytic because the same token is used.
(b) "Tully = Cicero" is also analytic because essentially I was just ignorant that they are two tokens that refer to the same Marcus Tullius Cicero of historical import.
The question of the reference of 'Tully' always depends under what circumstances the token refers to the same entity, and that is a matter of social convention; that is to say, it is normative. And the criteria for determining whether a sentence (NOT proposition) is analytic or synthetic is a function of evaluating the language game.
He explains it in the same paragraph:"The linguistic rules for using the name 'Cicero' and the linguistic rules for using the name 'Tully' are such that both names refer to, without describing, the same identical object...". You may not know the relevant linguistic rules, and then googling them up will be informative for you. But it is the same with "Tully = Tully" if you do not know them for "=". That a statement is analytic does not mean that it can not be informative or that it can not be discovered by empirical means. Only that it does not depend on anything empirical. – Conifold