First, the Passenger density doesn't have ANY effect on the number of passengers, because that's always the same, and it's calculated based on the airplane weight and can be overwritten if the "Estimate Passenger Number" option is disabled.
The density affects ONLY the number of people visible on screen at the same time, with the Sparse setting they are more spaced apart so, obviously, they will take LONGER to board but, it's always the same number.
About the number going up very quickly, as explained so many times on the forum, it's because passengers are only simulated if:
1) The gate doesn't have a SODE jetway or a GSX2/SODE jetway
OR
2) The gate has a SODE jetway, but is not docked
OR
3) The parking is in the open, but due to a wrong airplane configuration (usually a failure to set doors properly on an unsupported airplane), the Passenger Bus is not coming.