The simple answer is: yes.
Your examples above use modus tollens, one of the most commonly known valid argument formats. Deductive validity is about abstract format exclusively, not about the content of the premises.
The reason arguments involving conditional statements (as the ones above do) are valid or invalid here may help. What the first premise states is in the abstract format "If A, then B." What A and B are really expressing are necessary and sufficient conditions (hence calling it a "conditional"). What "If A, then B" asserts is actually a relationship between A and B. This is so no no matter what you're using for either (true, false, unknown, or nonsense).
In formal logic, the argument would run like this:
P1. A -> B (If A is true, then B is true)
P2. ~B ("Not" B - B is not true)
Therefore, ~A. (Not A - A is not true)
What's happened? A and B are asserted in (1) to have a certain relationship to each other in which A is sufficient for concluding B (A is enough by itself to show B's truth), and at the same time, B is necessary for A (B must be true, otherwise A is false, but B may not be sufficient). Since the second premise goes on to state that we "don't have" B - it's false - and the first premise asserts, in part, that we have to have B to have A... but we don't have B... it follows that we don't have A either.
So using one of your examples above:
P1. If God does not exist, there are no objective moral values.
P2. There are objective moral values.
Therefore, God exists.
A = God does not exist.
B = There are no objective moral values.
(These are both actually negated, and thus P2 and the conclusion would wind up being double negation, but that's complicating matters unnecessarily for an explanation, since ~~P (not not-P) is equivalent in truth to P.)
What P1 is asserting is that God's non-existence is sufficient for concluding that there are no objective moral values. At the same time, it's also asserting that the non-existence of objective moral values is a necessary condition for God's non-existence.
I highly doubt that P1 is true, because I don't think the relationship between the two holds, but that does not make the argument invalid. It makes it unsound.