it could help with the stutters, but it's better to take off the ps4 slim and check for the dust buildup, clean them off, change the thermal paste, and re assemble, and put the ssd onto it. it would help the game to not stutter.
Likely not. Modern games are designed to load as little as possible to get you in the game ASAP, then load in higher detailed assets as needed. If there's any stuttering going, it's likely something choking the CPU (keep in mind the CPU core in the PS4 was based off a netbook class processor)