It would only affect if your going faster than you believe, hence using more fuel.
But no, sounds like you have two problems.
Speedo not working will have 0 affect on actual petrol used, like none.
You've got another issue there somewhere!
What I'm saying is, if he is manually or even using the mpg read out, it wont be correct. as the car says he has covered 30 miles to 1 gallon. but, because the speedo has not been reading correctly, it will have covered say 40 miles to that 1 gallon. the MPG readout will say the 30 instead of 40.
get it fixed and see if there is abnormal fuel useage.
Trying to work out on the fuel gauge is a bad plan though. Go by what you fill at the pump not try and guess what is a quarter tank off the gauge. It's not accurate enough for that.