You realize that this is precisely what some people did, in the early Church, and for precisely that reason, right?
(Penance was a long and arduous process back then, and for a while, it was a “two strikes and you’re out” ballgame. So, rather than take chances that they’d be in the Church and then out forever, they put off baptism until their “sinning days” were beyond them.)
Hang on a second! You’re answering a different question than the one that @TheAdvocate197 has asked! You’re talking about a “baptism of desire”, but he’s talking about “lack of knowledge of Christ”! The two are not the same thing! A ‘baptism of desire’ refers to a catechumen who is anticipating the sacrament of baptism, but dies before he’s able to be baptized. (See CCC, #1259.)
On the other hand, Advocate is asking about someone who does not know Christ or His Gospel, but attempts to seek the Good:
The Church teaches that these, too, can be saved (see Lumen gentium, #16). But, the Church doesn’t teach the means through which this happens. I think it would be presumptuous to call this a “baptism of desire”, as well.
So, I would answer that this is not “a kind of baptism”, and therefore, does not remove the temporal punishment for sin, per se.
However, we might ask the question of whether that person actually committed sins that are imputable to him, if he had no explicit knowledge of God, or Christ, or the Gospel. The catechism talks about this “invincible ignorance” in its discussion of conscience and imputability of sin (see CCC, #1790-93). I think it might be possible to make the case that such a person could, in God’s judgment, be held not responsible for his sins. In such a case, then, there would be the question of whether the ‘temporal punishment due to sin’ applies.
So, I might think that the full answer to the OP’s question is “no, in the case you raise, it doesn’t seem like ‘salvation’ implicitly includes the remission of the temporal punishment due to sin; however, it’s possible that there might be none to be remitted, anyway.”