I used a Garmin InReach Mini for a 19 day trip down the Grand Canyon this past January. I checked in once a day to say "I'm ok" like you had planned to. I recharged mine about 14 days in since the battery was probably around 20%. It probably would have lasted the whole trip, but it was shockingly cutting it close. I didn't use tracking, had low brightness, etc but still found the battery life wasn't even close to the quoted life.
I found there are a two important factors to consider beyond the Garmin stated battery life:
- Temperature. There were nights when it was 5 degrees Fahrenheit with an average of high 20 something on my trip. Even though it was off at night this I think really hurt my battery life.
- Visibility of Satellites. I was at the bottom of the canyon, so I sometimes had some trouble getting a satellite signal. Sometimes over an hour. The longer it spends searching and trying to send a message the more battery you will use each time. If you are going to be above treeline with a clear view of the sky though then it will send in a matter of seconds.
If you leave it off and only use it for SOS you are set for months.
So while yes, it should last the full time of your trip, depending on where you will be consider a small (~2000mAh) backup battery.