Yeah actually it isn't obvious if the mod is working or not; expecially if you have not played vanilla.
An easy way to tell, I think, would be to get an ammo upgrade at the gun shop, and then see how much ammo you can carry.
Take for example the pistol. Normally, after an ammo upgrade, you can carry this much ammo (depending on difficulty level):
Ammo (after upgrade), vanilla:
80 Easy
40 Normal
32 Hardcore
24 Infamous
Ammo (after upgrade), Dylan's mod (adds +24):
104
64
56
48
To test without having to keep the upgrade, just save before you buy it, and then check the ammo (after going to the other shop and getting more ammo or a replacement of the weapon). Then reload.
BTW, I recently played 3 times in a row, once on Normal, Hard, and Infamous. Now I'm playing with Dylan's on Infamous. I think Dylan's makes the game easier (maybe too easy). You might want to consider playing vanilla first.
Have fun