...And to address the original question -
Burst tests and peel tests essentially test the seal strip weld strength, i.e. a strong weld could pass even if it's not properly sealing.
If you wish to maintain a sterile barrier then yes, leak test is recommended.
Please also note that as long as the barrier is not exposed to liquid, to maintain a sterile barrier, it doesn't necessarily have to be airtight (refer to the tortuous path principle; this is basically how Tyvek works as well).
Cheers,
Ronen.