You should.
It will help you with your writing and will find many errors. But it won’t catch everything.
It can’t identify logical progression errors where sentences and/or paragraphs should be rearranged, split or combined. In expository writing, it won’t identify weak topic sentences.
If you are writing a story, it can’t catch errors in character behavior or misuse of historical elements or parts of your story that contradict previous parts.
It may not catch broken or misplaced modifiers. Many of these are subtle and difficult to identify.
It will not always identify commonly confused words like emigrant or immigrant. Below are two example from my own writing.
Calvary or Cavalry
Kearney's exploits included many events within US history. He was associated with Kit Carson, found and buried members of the ill fortuned Donner Party, and wrote the Kearney Code. He has many locations named after him. He is also called the Father of the United States Calvary. And that is where our story as Iowans begins.
The word Calvary can be easily swapped with Cavalry. This mistake can really irate readers when you use the mount upon which Christ was crucified when you meant to refer to mounted Army units. Bad, bad mistake.
Canon or Cannon
Off in the distance came an army. Horse-drawn artillery canons led the formation. Attached to some canons were limbers and caissons. Several different types of barrels and muzzles all squeaked upon their carriages. Adamina believed there were at least a hundred if not more.
Grammarly should have really caught this error due to the use of the words army, artillery, limbers, caissons, barrels, and muzzles. These are all associated to cannons used in war not to some canon of literary works. But it didn’t, an editor will.