Cannot deny this possibility. Increase in Fee has led to lowering of cut-offs in the past. At the same time, reason behind that could also be the difficulty level of BITSAT being higher in that year.
IITs increasing seats by 1000 should have some impact on BITS cut-off but we have see if this increase in seats in IITs is across all branches and across all campuses or not. e.g. increasing seats in core and old branches at old IITs will surely have an impact on BITS cut-off but if this increase is due to addition of new branches or increasing intake in newer IITs, it will not have much impact on BITS cut-offs. But even if there is going to be any impact, I think it will not be huge. (Should be somewhere around 5-10 marks in my opinion)