The first hurdle was actually getting to my class missions while I was at such a low level. As you can see in the above screenshot, the mobs in the areas leading up to my missions were 7 levels higher than I was. This makes it impossible to solo. You can't hit opponents that are that much higher than your level. Every shot was a miss. But I had a level 50 gladiator dragging me along, so one-shotting these level 22 mobs was no issue.
Then obviously the missions themselves involved fighting elite level 21 mobs. If you're level 15 and alone then this in itself is absolutely impossible. Even if you work out a way to get to the mission, whether it be via stealthing or clone zerging, you'll have no chance to kill the level 21 elite at level 15. But there is nothing stopping you from bringing a friend. Rammy, my gaurdian, got one or two shots off; before this bounty hunter had a chance to blink he was dead.
I levelled from 15 to 16 in just a couple of missions, so our experiment to see if I could get Bowdaar at level 15 became moot anyway.
To complete all my class missions on Nar Shaddaa it took the two of us working together about 45 minutes. I leveled from 15-16 and Bowdaar became my companion at the end of the quest line on that planet. I was also pleased to see that Bowdaar's equipment was rated much higher than any standard level 16 equipment; in fact the mods in his weapon are level 21, even though he is only level 16.
I have since gone back and completed all the missions on Corellia and Taris (both of which I had skipped for the experiment of teaming up with a level 50) and having an over-equipped tank has made the missions extremely easy.
There is absolutely nothing stopping you from powering through your class missions with the assistance of other players, even if your class missions are on space stations or space ships. Your group members can land and join you on those stations and ships to assist you in any fight.
Obviously, as you complete your class missions, you not only get the benefit of higher level companions joining you, but you also get access to higher level equipment that is a class reward and usually has no level restriction.
Although I don't recommend you do this for your first or even your second experience in SWTOR, once you have a few alts leveled up, this could be a quick and easy way to level an extra alt for crafting or different experiences.