More or less. Essentially, the name of the game in much of Aquinas's "proofs" is to define God as existing, via the circular route of defining God as being equivalent to some thing already known to exist, or to some thing that is thought must inevitably exist. The fact that such a definition becomes a one-off when done in such a manner only serves to obscure the fact that one is simply defining God as existing - like all
petitio arguments, it is, at its core, a tautology. Ignoring the other holes in the First Cause argument - and there are several - one can readily illustrate the absurdity by preserving the logic, such as it is, but changing the particulars:
P1: God is an apple tree in my back yard.
P2: The apple tree in my back yard exists.
C1: Therefore, God exists.
And so forth. Tomorrow, the fallacy of accident will be the topic - the First Cause argument also serves as a reasonable illustration of that fallacy as well.