Yes, you can do that. I would suggest not staggering the start times. Put all on at once, brisket on the bottom, fat side down of course, ribs on top.
When the ribs get nicely, richly colored (this will depend in type of ribs, come-up time on the heat, and cooktemp - 90-150 min, probably) foil each rack separately, meat side down, a little juice or juice reduction (my pref) splashed in. Retun the ribs to the cooker and cook till tender while in the foil.
Meanwhile, foil the brisket at ~ the 2.5-hour mark, or ~165?. No matter what state the ribs are in at that time remove the entire grate containing the ribs to a side table, remove the brisket, replace the lid, foil the brisket, then return all to the cooker.
When the ribs are tender (check the first time about 40 min after foiling) remove them. Open the foil to ;et them cool, retaining some of the foil juices for your sauce, if desired. Carefully transfer the brisket to the upper grate.
When the brisket is done allow it 10-15 min rest then return the ribs to the cooker to firm the bark, several minutes. Platter the ribs, slice the brisket; serve.