Using AC-DC converter Module
Yes, no problem doing both at the same time it's often done that way.  If you are selecting the capacitors make sure they are safety rated X and Y capacitors.  (If you don't know what that means make sure you research it prior to hooking anything up.)  Also the value of the Y caps between hot and chassis ground should be such that if the chassis is somehow ungrounded there is not enough leakage current to present a shock hazard.  There are regulatory requirements around that and you should understand those as well before selecting the caps.  Another option is to buy an off-the-shelf EMI filter that includes the proper components.