No, as long as you don't erase it there is nothing to worry about.
The only three things that can be trick:
1) If Filevault was enabled on that SSD, will macOS present a pop-up asking you for your password to unlock the SSD, or whether you will need to manually unlock/mount it using Disk Utility. The password to unlock Filevault on that SSD will be an admin password from that broken laptop.
2) Will the "Users" folder on that SSD be easily accessible by showing on the Desktop or Finder's Sidebar if you have it configured to automatically show mounted external volumes, or whether you will need to navigate to "/Volumes" to access the "Data" volume which will have a "Users" folder with your accounts from the broken laptop.
/Volumes/Data/Users
If you see an empty "Users" folder, then you will need to go to Disk Utility and manually mount the "Data" volume for the external SSD.
3) If you see the "Users" folder for the SSD of the broken Mac, do your macOS user accounts align with those on the old Mac so that you have the correct macOS permissions to access the contents of the home user folder of th external SSD. Personally I don't like to modify the file/folder permissions of any boot drive until you know that you no longer will use it for booting. If you don't have access to the contents of the home user folder, then perhaps a second macOS user account on your good Mac will align & allow you to access those items. If not, then using the third party app Carbon Copy Cloner (CCC) is an option (there is a free trial period) which will allow you to access the contents of the home folders by prompting for an admin password to elevate to admin privileges to bypass the permissions issues. CCC also allows you to select & deselect items you wish to copy & retrieve from the SSD. CCC has been around for decades and its developer is well regarded in the Apple community.
Here is probably the easiest method, but requires access to another external drive:
Since you have a working 2015 MBPro you could boot from that external SSD and transfer the contents to another external volume. To boot from the external SSD from the broken laptop, hold the Option key immediately after hearing the startup chime so that you can access the Apple boot picker menu. If the SSD from the broken laptop is already connected you should see it as a boot option with an orange icon....you can connect the SSD from the broken laptop after you reach the Option boot screen and it should show an orange icon after a few minutes.
Or while booted from the external SSD you can transfer the data to the "Users/Shared" folder for the internal drive (when booting from an external drive, the internal "Users/Shared" folder will be available at "/Volumes/Data/Users/Shared" (may have same issues as noted above regarding Filevault and mounting of the Data volume), but you won't have the permissions related issues at this point in the transfer:
/Volumes/Data/Users/Shared
It is up to you whether you boot the working 2015 laptop with the external SSD from the broken laptop or whether you just boot the good laptop normally and access the external SSD as a regular data drive. Unfortunately with macOS behaving differently for different versions of macOS when trying to access another macOS boot drive it is hard to be more specific until you make the attempt & provide details on where you get stuck. At least you go into it having a bit of knowledge of the things you may encounter while trying to access the data on the SSD. As long as the SSD is good and its file system is good, then we can help you access the data on it.
Good luck.
