Consider the question expressed in the title: *Does theism imply worship?"
The answer depends on how one defines "theism" and "worship". If a mere rational acceptance of the existence of a God is called "theism" and if that is all that is needed for "worship", then theism does imply worship and the answer would be yes. However, if worship requires more than a rational acceptance of the existence of a God, then the answer would be no.
Wikipedia describes "worship" as the following:
Worship is an act of religious devotion usually directed towards a deity. An act of worship may be performed individually, in an informal or formal group, or by a designated leader.
The word is derived from the Old English weorþscipe, meaning worship, honour shown to an object, which has been etymologised as "worthiness or worth-ship"—to give, at its simplest, worth to something.
This description is broad enough to include mere rational acceptance since acknowledging existence could be considered acknowledging the "worth" of something.
To try to find some forms of theism that might not involve worship one might look at those who profess a form of "philosophical theism".
Wikipedia describes philosophical theism as follows:
Philosophical theism is the belief that a deity exists (or must exist) independent of the teaching or revelation of any particular religion. It represents belief in a personal God entirely without doctrine. Some philosophical theists are persuaded of a god's existence by philosophical arguments, while others consider themselves to have a religious faith that need not be, or could not be, supported by rational argument.
For some of them, such as Christiaan Huygens listed among the notable philosophical theists, science or rationality itself may be viewed as a kind of worship:
Christiaan Huygens (1629 – 1695) was a prominent Dutch mathematician and scientist. Huygens was first to formulate what is now known as the second of Newton's laws of motion in a quadratic form. He regarded science as a form of “Worship”, that is, one can serve God by studying and admiring his works: "And we shall worship and reverence that God the Maker of all these things; we shall admire and adore his Providence and wonderful Wisdom which is displayed and manifested all over the Universe, to the confusion of those who would have the Earth and all things formed by the shuffling Concourse of Atoms, or to be without beginning."
One might try to separate theism from worship by describing theism as an indifferent rational acknowledgement of God while describing worship as a more committed and personal acknowledgement of God. However, given a broader view of the idea of worship as "worth"-ship, one could also argue that just rationally acknowledging the existence of God is a form of worship.
Wikipedia, "Philosophical theism" https://en.wikipedia.org/wiki/Philosophical_theism
Wikipedia, "Worship" https://en.wikipedia.org/wiki/Worship