No, the portable CWS310 will not be able to power a TM-T88x printer by the built in battery - there might be a solution in the future, but currently no powered printer available.
Depending on the use case, customer may use the
400490-261-PT Epson Mobilink TM-P60II WiFi portable receipt printer with battery and power supply
or (if there is no WiFi - but still you will need the WiFi version of the 310 for this)
400490-262-PT Epson Mobilink TM-P60II blue tooth portable receipt printer with battery and charger
C31CE14551-PT Epson TM-P20 bluetooth portable receipt printer with battery and base charger: black
Both solutions might have advantages and disadvantages, I would recommend to open an engagement with your Pre-Sales team to narrow this down to the needs of your customer.