...will the SSD speed up my computers' performance as well as increase it's capacity OR will my expensive upgrade still leave me with a slow computer?
The 2015 MacBook Pro came with an SSD, so the only thing you'll do is increase the storage capacity, not improve the performance.
However, this sounds like you're just throwing parts at the problem in the hopes of solving it. What you need to do is isolate and identify the problem causing the slowness:
If your SSD is full, it could contribute to the performance issues. In this case, adding a bigger SSD would benefit.
Take a look at your Activity Monitor - memory and CPU. See what's consuming either/both.*
Try doing a clean install (wipe the drive and do a fresh install of macOS)
Make sure you have a Time Machine Backup.
* Whatever results you get from here, search this site prior to asking a new question because this topic has been asked/answered numerous times previously and you're likely to find your answer there.