The answer is no, you may only camp in designated areas. Camping is only allowed in designated areas at Jasper park. If you contact the park directly by e-mail the answer is the following:
In Jasper National Park, when hikers are hiking on trails they must camp in the designated backcountry campsites only.
From the official Parks Canada Backcountry Guide in Jasper National Park 2013 you must
Obtain a Backcountry Camping Permit from a Park Information Centre.
and from Parks Canada Jasper section
A backcountry camping permit is mandatory for all overnight trips and can be obtained by phoning the Trail Office (780) 852-6177.
These permits are obtained for specific campgrounds and/or designated sites.
In Jasper, exceptions exist for climbers which allow them to bivouac in specific cases. You still need to obtain a backcountry camping permit.