I would hazard a guess that the main problems with DECT repeaters would be where manufacturers have chosen to exceed the basic DECT/GAP procedures with proprietary enhancements such as caller display and answer phone playback. Don't know if GAP includes these or not, nowadays?
I have quite a large collection of different DECT phones, mostly from different manufacturers, and different ages. All are GAP compatible and so, with a little effort, all can be made to register with a single base and they always do work together for basic telephony. But for the cleverer stuff like caller id, phonebooks, and answer phone, it hardly ever works unless everything is same-brand, same product family.
I notice some claim to do seamless handover, when you move around the house. At back of my mind, I didn't think that handover was in generic DECT? In which case again, it might only work with some phones.
For basic call handling then if it were me, since I like playing with DECT, I might be tempted to buy one and try it regardless of whether it is 'supposed' to work. My guess is it may actually work quite a lot. But you'd have to accept the significant risk of it not being successful...