Simple answer is yes. 

However, after that it very much depends on the brand and model for compatibility and ease of use. They are not all the same. So I'd check out whatever I was thinking of buying before I bought it.

If you're not aware there is a CT app which may suit your needs better. 

TBH i find it easiest to down load my CT routes to my PC and then use file explorer to load to Garmin.  100% success where as friends who try to use the Garmin process seem to have a lot of issues.  The app is good but of course does use up phone battery so depending how far you are going have a basic Garmin may be better and is my choice

I used CT for the first time last September, for 3 weeks in Brittany. I generally used the internet version on my phone rather than the app, as that gives you height gains. I then sent it to Garmin Connect (on my phone), which I then sent to my Garmin by bluetooth. It worked really well. 

When saving a route, I'd add 'CT' or 'GM' to the title, to show how it was created - perhaps by Google Maps. 

Sometimes I'd create a choice of routes for a day, to see how they compared. Then I'd put a star next to the one I intended to use. It worked really well. 

It's worth using more than one route creator. For instance - and to our surprise - CT didn't provide a wonderful route using a ferry to the south of Vannes, nor did it find an absolutely fabulous tarmaced old railway line running north into Ploermel. Google Maps found both these routes. The latter was many, many km long, a gradual ascent, with virtually nobody using it. An absolute delight. I wonder if Richard F might be able to comment on this? 

But overall, we really enjoyed the quiet backroads CT gave us.