Yes WordPress Storelocator Plus is compatible with the version of PHP you are currently using. (5.4 or higher)
It IS very much encouraged to run PHP 7 and up. The author has published a few articles on the subject.
His article about SLP and PHP here may be of interest.
Always Make sure you back up your site before any major changes. (we use Jetpack)
Here is Another technical article about updating your Configuration.
P.S. SLP is now at version 4.9.6, Power is 4.9.4
Thanks for the kudos. I will pass it along to the developer and author. He would really appreciate the review if you could rate the plu here.