Can a 7 speed Derailleur work on a 8 speed cassette
8 speed shifter and cassette, 7 speed derailleur? You'll be fine. There's no "probably" about it.

6-, 7- and 8-speed gear is all cross-compatible in terms of chain width. 

The only time you'd hit a problem is if the shifter and the cassette weren't made for the same number of gears, for example you could imagine a scenario (e.g. 7-speed cassette, 8-speed shifter) where you might click past the edge of the cassette. That would negatively impact your day.