No no. 
Lets say you have a single army of 10k, and you claim a territory. That would raise the total number of troops you could have in your nation in total, not that army, and it would not grant an immediate extra 5k soldiers. 

A better example would be if you attacked with an army of 20k, your maximum possible army size. You claim a territory, and your army cap goes up to 25k. You would still need to keep adding 2k soldiers per season to get up to that max.