The answer is: YES! Most sergers have a specific order to the threads, and if not followed, there's a possibility the machine will never work properly. You should consult an owner's manual for your machine, but most machines should be threaded:
Most Important: Always RAISE the presser foot when threading the machine. This releases the tension disks and allows the threads to seat properly. Also, when threading, give each thread a little tug going through the disk to confirm it is seated all the way--sometimes it will actually make a little "pop" when it seats.
Something you can try is install brand new needles if they are causing a problem. Needles should be changed frequently as they wear and are damaged through regular use.
Here's the threading order for a lot of machines. First thread the upper looper thread, then the lower looper thread with the thread tail "draped" over the top of the upper looper in its final threading process before threads being pulled under the presser foot and toward the back of the machine. Needle threading is usually not as important in the threading order process, but they should not be twisted and their thread paths should be correct.
Of course, be sure to pull at least 6 inches of thread tail so the threads are not pulled out when stitching is begun.
The Anatomy of The Best Serger Tension My Tips Bonus Unpick it Serger...
Make It Handmade Threading Your Serger or Overlocker
Lower looper woes on my serger