No, not usually. Personal taste though. There are times when the fat is very thick on the flat and the point end and the hollow between the flat and point. If any of this is the case I'll trim some, maybe 1/3 - 1/2 of it, prior.
When you cut the brisket into strips (which you have to do for the meat to fit into the grinder), cut the strips in such a way that the fattiest strips are mostly fat with a little lean, and the lean strips are mostly lean with little to no fat*.
If you prefer finely ground meat the above isn't necessary since you'll be grinding twice or thrice anyway, but if, like me, you prefer some texture, this will set you up for that.
Chill the strips in the freezer for several minutes till firm, on a parchment-lines sheetpan. Grind the fatty pieces first, onto a small sheetpan or into a bowl. Move to the side. Using a larger bowl, grind the lean pieces one at a time, adding some of the already ground fatty mix to the hopper at the same time. This process grinds the lean once, the fat twice. Since brisket fat is quite firm, grinding it twice makes is more able to soften/render during cooking; grinding the lean once retains texture.
* Imagine a packer in front of you on a cutting board, fat side up. Cut the roast crosswise into 1.5-to-2-inch strips or so. Take a strip and turn it on its side. You'll now see the edge of the fatcap on one side of the strip. Cut that off, taking a little lean off with it. That's your fatty strip. The piece remaining is your lean strip. Repeat with the remaining crosscut pieces - there you go.
Note: If you buy packers but prefer to smoke only the flats you can separate the two before smoking, stashing the point for grinding into burgers. Since the point alone tends to have a higher fat ratio you might want to trim off some fat (or not) before grinding.
Many supermarkets sell overtrimmed, thin flats. Though not great for smoking, imo, all is not lost. Grind them with some chilled-till-firm bacon strips to add back some needed fat, and fashion burgers from that mix.
Ernie-- If you have a food processor you can 'grind' your own meat. The process is a bit different but it works.