The answer is usually no, but it can depend on a lot of things:
1---What kind of variegation?
-- -- -- -- outer leaf edge
-- -- -- -- interveinal or veinal
-- -- -- -- spotting
-- -- -- -- streaking
-- -- -- -- regular or irregular
2---If the "naturally occurring" variegated plants grow that way from seed, than there is a better chance that the trait will show up in at least some of the offspring. Generally speaking with flowering plants, if the variegation originated from a growth on a non-variegated plant, the trait will not be transferable sexually (by seed).
