If I were to do a blue/white selection of transformed E. coli on LB agar ampicillin plates at room temperature (23⁰C) for about 2 days and 18 hours, will I run into the issue of satellite colonies or any other issues?
Since b/w screening is a means to selection, you want maximum selection pressure. This will be obtained by incorporating all optimal conditions. The many enzymes of the lac operon are going to function best at their optimal temp.
Why would you do this? If it is because you can't go in the next day it's better to do it when you're available. You're only going to doubt your results when you get them.