Short answer to your question is: No.
Here's one of the best summaries of the DEC regulations and guidelines for the High Peaks Wilderness Area (HPWA).
http://www.adkforum.com/showpost.php?p=249024&postcount=1
The eastern half of the HPWA has more stringent regulations than the western half (where you plan to hike). For example, in the eastern half campfires are forbidden, bear canisters are mandatory, dogs must be on leash, etc.
For camping, you can camp at free, first-come-first-served, DEC
designated campsites (marked with a yellow "Camp Here" disk) or
primitive-camp a minimum of 150 feet from roads, trails, sources of water, and structures like lean-tos and DEC Outposts. In addition, you're not permitted to camp above 3500 feet unless it's at a designated campsite (all the designated campsites in the western HPWA are
below 3500 feet).
Designated campsites near the Seward Range:
Along Calkins Brook Truck Trail.
East of Blueberry Lean-to.
The woods along the Blueberry Trail, Calkins Brook Truck Trail, and Ward Brook Truck Trail, are fairly open and flat. You shouldn't have a problem finding suitable terrain for primitive-camping (that is at least 150 feet from the trail, water, etc). The land
across the trail from the Ward Brook Lean-to is a good tenting spot (and not the illegal sites behind the lean-to that are all too close).
On the other hand, if I was going to circumnavigate the Sewards, I'd opt for camping in the lean-tos along the Cold River. That area sees little traffic and you'll probably get a lean-to all to yourself. They also have handy firepits.