Space heater or no space heater I don't think it will make one bit of difference by requiring the receptacles to be 20 amp receptacles. You will not find many (if any) portable space heaters intended for household use with a 20 amp cord cap. If you have same number of outlets and same 20 amp breaker you can still plug in same combinations of loads if they all have 15 amp cord caps on them.
The heaters that are load killers on branch circuits are the ones that claim they can not start a fire, are usually in an "attractive" oak cabinet, and "use no more energy than a 'Mr Coffee'". What they don't tell you is that most people that use a "Mr Coffee, do not brew coffee all day long, as there would be a noticeable difference in energy used if you did that vs. just a pot or two every day. And don't believe they can't start a fire, I have replaced more than a few melted cord caps/receptacles on these units, 1500 watts through a poor connecting receptacle doesn't care what is at the other end of the cord it is going to get hot anyway.