The answer is Yes and also No.
Yes because a taxonomy field can be set to save and load terms. This will do what you want.
No because you have the taxonomy field in a repeater and this causes save and load terms to not work correctly.
In order to do this you need to do 1 of 2 things.
1) Rework the site so that you do not need a repeater.
2) Add custom PHP code to the site to correctly save terms. To do this you need to create an acf/save_post filter. In this filter you would loop over the repeater and collect a list of terms and then use the WP function to set the post terms.
