The size of the duct coming to the boot is the most important factor in determining how much air will be delivered to any supply device so the short answer to your question is no no negative effects you will have less air noise but essentially the same volume (cfm) you are wrong however about that supply not being important, keeping outside air out is of the utmost importance and doors are one of the biggest infiltration points.

Here is a link that might be useful: Air Conditioning Repair made Easy

Miken is correct concerning the air volume being determined by duct size & velocity.

We don't know what CFM volume is coming to the boot.
Let's say it was 100-cfm, many 4x10 floor diffusers' with a Face velocity of 600-fpm, would have an "air-discharge throw" of 9'feet & spread of 5.5'.

A 6x12 @100-cfm with a face velocity 300-fpm has only a 4' throw, spread 6.5'.

The 6x12 would need a 130-CFM with a face velocity of 400-fpm to achieve 8.5' throw with a 5' foot spread.

The terminal velocity from those diffusers' is 50-fpm.
For duct sizing view linked page
- udarrell

Here is a link that might be useful: DUCT SIZING CHARTS