2 1/2" chambers are frequently English guns. It was the standard size, and 2 1/2" cartridges are widely available here. What you should be aware of is that 2 1/2" is a 'nominal' figure.
There are several factors as the different gunmakers used different actual chamber lengths and different forcing cone profiles. Also the older guns were designed with roll closure cartridges being the norm. These are shorter than crimp when opened.
Many nominal 2 1/2" chambers are actually more like 2 5/8" and have gentle cones, so are quite tolerant of a cartridge greater than 2 1/2" when opened out.
However some have short sharp forcing cones, starting quite near 2 1/2".
Therefore it is not safe to generalise and say only a small pressure rise will occur using the longer cartridge. That may NOT be true in all guns. Each gun needs to be considered separately.
I know of a case where a nice Boss gun was put off the face by a day shooting 2 3/4" cartridges that were within the load limits of the gun proof (1 1/8 oz) but just too long a case - and the high pressures caused damage.