It can, but you'd still be getting it to fire, it would just sound rough and backfire, etc.
If it wasn't such a PITA to unbolt the downpipe, you could just do that and try starting it.
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'13 Mustang 3.7V6 - MT82
'00 GP SE (L67 Swap, XP, Headers, 3.25")
'98 GTP, '01 Bonne