Travis, I brought my boat along on the trip I did this July. In summary:
I'd be surprising if any of the rivers/streams on the island are boatable, even in a packraft. Maybe at the peak of spring runoff, but doubtful.
The interior lakes, exterior beaches, and chains of islands on the eastern end would make for some very interesting packrafting opportunities. A hiking and packrafting trip on Isle Royale is firmly on my to-do list.
You'd certainly have to be very careful with the weather, especially out on Lake Superior itself. Packrafts are slow in a straight line, and small. Big crossings would be commiting, and put you at risk if wind blew up suddenly.
Here's my vague plan for a future trip, starting and ending in Windigo. Ideally I'd like to go in autumn, just to see the island then and be away from bugs.
-Walk the Feldtmann Ridge trail to Rainbow Cove, then walk the beach and packraft the headlands all the way around Point Houghton to Siskwit Bay. On our plane flight in the beaches from The Head to past Long Point looked like they'd made for good travel.
-Hike the Island Mine trail up to the Greenstone, then over Mount Desor and down to Lake Desor South. Packraft over to Desor North, hike to Little Todd Harbor.
-Packraft and bushwack to Todd Harbor along the coast.
-Hike to McCargoe Cove.
-Packraft, portage, and bushwack through Pickerel bay, Lane Cove, Stockly Bay, and Duncan Bay to Duncan Bay Narrows CG.
-Hike the Greenstone to Mount Obijway, then down to Daisy Farm.
-Paddle across Moskey Basin, then bushwack and paddle past Wallace Lake and Mason Lake to Chippewa Harbor, Lake Wittlesey, the coast, and Malone Bay.
-Hike up to Ishpeming Point, down to Desor South, cross the lake again, hike the Minong back to the end and go home.
The idea is to hit the best trails, the most remote regions, and good high points. Boating and hiking when it makes sense. Presuming that most winds will be coming from the west(ish), open water travel is designed to be in an easterly direction. Of course, you could hit a week with crazy winds and the whole trip could be much harder or impossible. It could also be really, really cold in the boat.