The short answer to this question is NO, partially for the reasons Clifford described and partially because of the change in angle of the chain between the ring to the cog. The bigger answer though is there's usually enough slack to accommodate a few different cogs with a few more or less teeth. And the even bigger answer is you're thinking about this wrong, because if you are considering changing chain rings and changing FG cogs, you're going to get involved in some time consuming labor that will make chain length adjustments seem quick and easy. I suggest finding the crank you like, use whatever chainring it has on it, and then just experimenting with different cogs - that's what almost everyone does.

You don't have horizontal dropouts, you have track ends. Might as well learn the jargon. Welcome to the club.