Return air ducts need to be sized in proportion to their respective supply ducts. If you tie in new return registers to existing return ducting you stand a very good chance of unbalancing your system and making inter-room temperature differentials worse. In other words, yes, adding return registers to existing ducts could cause the upstairs registers to lose suction.
Return air imbalance issues involving closed rooms tend to confuse the heck out of HVAC contractors because they're not familiar with the problem.
Because you've implied that you're having problems cooling the entire house, your best option is to do a full Manual J and Manual D workup for the entire house before cutting or installing anything. Compare your Manual D duct sizing results with what's actually installed and correct as necessary. Installing returns blindly is unlikely to fix your problem.
If you're not comfortable putting in the time and money to do the Manual J and D work yourself (it's not easy), then hire an engineer to do it for you. Engineers are usually cheaper than trial and error alterations.
Finally, be advised that even temperature control in a multi-story house is a hard problem. Expect to need to re-balance your HVAC system (using dampers) when you switch between heating and cooling seasons.