Can long term use of methylphenidate in adults cause depression as a side effect? Would antidepressants help with that?

No evidence. There is no published data showing a link between the two. Antidepressants can be very helpful.
Apathy mainly. Methamphetamine causes depletion of Dopamine from the brain more than other neurotransmitters. Low Dopamine is associated with apathy which can resemble depression. Low serotonin is the major underlying cause of depression. Low norepinephrine is a cause for fatigue. All these neurotransmitters are affected by "meth" but the main one is dopamine. Most anti-depressants don't target dopamine.