Some SAS procedures use the formats, others ignore them. So the answer is: It depends.
For instance, PROC MEANS uses formats for the CLASS statement but not for the VAR statement. FREQ uses them throughout. REG ignores them for continuous variables. The DATA step generally ignores formats in expressions, but there are functions to allow you to get the formatted value [PUT(varname, format.), for instance].
You probably need to read the chapters on Dates and formats in the Base manual and scan the procedure manuals for 'format' in the PROC chapters that are of interest. For us to provide more specific suggestions, we'll need a more specific question.