No, you cannot get full body greywing rainbow chicks; to do so, you would have to have one parent either split or visually clearwing and the other either split or visually greywing; FBG is caused by the co-dominance of clearwing and greywing. Because the mother is dilute, and dilute is recessive to everything, she only has two dilute genes so all babies will be split dilute. However, you can get rainbow babies. Clearwing rather than FBG is also considered a "rainbow" mutation.
Their babies would be skyblue, yellowface II, and opaline, which already is most of the rainbow mutation.
The possible outcomes are as follows:
Sky blue, yf II, opaline, greywing /dilute--visually greywing (50%)
Sky blue, yf II, opaline, clearwing /dilute--visually clearwing and therefore rainbow (50%)
Dilute is recessive to both greywing and clearwing. Greywing and clearwing are both recessive to wild-type (normal) but dominant over dilute, so although all chicks will be /dilute, they will show visually either greywing or clearwing due to the father being full body greywing.
Have you bred budgies before?