I don't know that section of the river specifically, but i was in glacier this summer and camped at two medicine. My understanding is that the section within the park does have cutthroat but the fishing isn't anything special. Mostly smaller fish but they are there if you want to wet a line. I did talk to some guys at a national forest campground just outside the park and they were doing a seven day backcountry adventure in whatever national forest is near the indian reservation on the east side of the park. One of the rivers they were hiking into was the two medicine and they said the fishing was very good with larger fish available.
In my experience the better fishing in the park is in the lakes. i hiked into a few while i was there and found some very good fishing. Like almost too easy to be interesting type fishing if you can find one that is populated primarily by cutthroats.
i did hike into upper two medicine lake for an overnight backcountry night and found some decent fishing for brookies. Nothing huge but some decent fish. You could easily do it as a day trip if you wanted as the hike is only about 5.5 miles but very flat. There are supposedly lake trout but i didn't catch any.