Maybe.
If you want a better answer, better details are needed.
What R4i do you have?
-- There are about 30 carts out there calling themselves 'R4i'. Some work with DSi 1.3, some 1.4, fewer with 1.4.1.
What DSi firmware are you on?
-- Newer DSis come with 1.4 and could possibly have 1.4.1 if Nintendo is shipping those yet.
I would highly suggest buying a non-R4 card since they're all fakes.
At best you get a clone that is supported by wood.
At worst you get a clone that isn't supported, period.
Get an AceKard if you just want a cheap card (will need to be flashed for 1.4/1.4.1 on a DS/DSLite).
SuperCardDSTwo has processors on the chip for SNES/GBA emulators, but sucks up power and is expensive.
iEvolution from CycloDS is coming out soonish(?), but they've not been the greatest when it comes to timely updates. They also tend to be far more expensive than anyone else.