Yes, but Engineers have infinite ammo.
The problem is, they're fairly restricted in terms of what weapons they can use. You basically either go CQC or Carbine--that's not to say that there aren't good carbines or that you can't get excellent TTK with shotguns and SMGs, but the former are generally inferior to ARs and the latter only work in specific circumstances. Additionally, when you're lone-wolfing, health is flat out more important. With most Medic weapons and decent fire control you can squeeze out at least 2 kills per magazine, fewer if you're spraying all over. Contrawise, if you can't self-heal, the first time you fight someone who has a chance to fight back long enough to do health damage, you cripple your ability to keep fighting, because the next person to see you will probably be able to kill you.
A LW Medic needing to pull back is a Medic who's killed enough people to run dry on ammo. A LW Engineer needing to pull back is an Engineer who had someone shoot at them and hit.
On a related note, most of the Engi kit isn't really about small-group or 1v1 infantry combat. Your special ability is pretty much useless in those situations, your utilities are only useful if you thought to bring AP mines (which rely on foolish/unlucky enemies rather than your own skill), and you can't do anything to assist teammates in small skirmishes in the way the Medic can.
That's not to say the Engineer doesn't have a niche beyond driving/piloting, but it tends to be confined to supporting MAXes, spamming rifle grenades to break up clusters and corner-campers (which, sadly, has been heavily nerfed in multiple ways), and suppressing or sniping vehicles with the turret. It used to be my most-played class back in the day, but then they hammered UBL damage and splash into the ground without fixing the glitchy reload and rearm that sometimes prevents you from resupplying or reloading them.