Does mountain biking 10miles a day make you a faster sprinter?
Probably only if you start from a very poor level of fitness.
Bike riding is mainly about endurance, while sprinting is all about
explosive power.
There can be secondary benefits though, if the added exercise of
the bike riding is enough for you to lose some weight, then that
will help in sprinting. If you use the bike riding for interval
training(i.e. go flat out for a short period, rest a little , then
go flat out again) then it can help a little too.