Nah you cant fire anything using their specials except mega guns, and AA attacks. Same goes with outlaw, brimstone or shadow (secondary). They are locked out of using weapons whilst specials are going "pew pew"
This is one "drawback" to the gameplay IMO, from TM2 to TMB era.
Tm2 you could use multiple weapons at the same time, combinations. 2 Thumper specials at once, or even a power missile during Mr Slam's special w/ mines and driving backwards.
HOWEVER. A clever girl can get around this because TMB has insanely different missile speeds. Some are slooooower, others are fast.
So you could land a reticule, a freeze, a special, a ram. ALL at once. So the ret is slow, fire that and freeze first... turbo towards enemy, fire special and ram? All four land around same time = uber damage.
Obviously with TMX, most weapon speeds are pretty much uber wtf fast, so these strategies don't come into play. If they do, its minimal.
This is part of the reason why the weapon speeds being soooo fucking overclocked in TMX helped kill combos and make the game a spamfest.
The bigger reason was that it helped nuke dodging and driving. Of course