Only to the extent that the RD can take up the chain slack when running in the granny ring, or that the RD can physically clear the big cog.

If the bike has an MTB RD, no problem at all running MTB cassettes--or road cassettes for that matter. Shimano 8-speed (and most 9-speed) is mix-and-match (within the speeds) so it's no problem running STI shifters with MTB RDs. Touring riders do it all the time.

If it has a road RD, when running in the granny ring it may not be able to keep the chain tight beyond about the middle of the cassette (say, the 15-tooth cog) because of the extra chain length required to fit around the big cog. At the other end, if it physically doesn't clear the big cog, the B screw may provide adequate adjustment.