SiS 6speed cog to 7speed cassette

I'm considering picking up a new (actually they're lightly used with 600
miles on them) set of wheels for my '88-'89 Specialized Sirrus (this bike
dates to when the specialized Sirrus was still a road racing bike and not a
hybrid/comfort bike); however,
it's equipped with the original Shimano 105 SIS six speed freewheel.
Would it be possible to run a seven speed cassette with my original
deraileur and shifter's if they're set to friction mode? Would I have to
make any changes? Specifically would I have to change my chain or
deraileurs?