Grammarly will not rank up your article’s keywords at all, but it may help with ranking up your website in general.
Having your articles written in perfect (or as close to perfect as possible) grammar will help with your rating, as Google labels sites with poor grammar as lower quality. However, you may not even need to buy Grammarly in order to take advantage of that function. The free version does a pretty good job at ironing out your grammar.
If you’re outsourcing your writing (or rewriting existing articles yourself), then the Premium version of Grammarly could help you with its built-in plagiarism checker. But please keep in mind that Grammarly is not Copyscape, and its plagiarism checker is simply not the best one out there.
All in all, only buy Grammarly if you think that it could improve the quality of your content. It won’t really do anything about keywords. If you’re interested in ranking up your keywords in particular, you’ll probably want to use a tool that was designed for that purpose. Just look around, the info is everywhere on BHW.