TRÅDFRI Wireless control outlet do they act as a repeater

They do, but they are not great, at least not unless you have loads of them. Checkout recommendations
and tips here → Guide for Zigbee interference avoidance and network range/coverage optimization

If you want the best setup that does not cost much more then highly recommend getting three (or more) Sonoff ZBDongle-P or Sonoff ZBDongle-E adapters to use in USB-chargers for power after converting them into dedicated Zigbee repeaters / range extenders by flashing Zigbee Router firmware.

Otherwise, the IKEA Trådfi Signal Repeater is relatively good for an out-of-the-box soluution (and that works better as a dedicated Zigbee repeater / range extender compared to for example the IKEA Trådfri Control Outlet), the CC2652P and EFR32MG21 based ones with external antenna like those Sonoff ZBDongle-P or Sonoff ZBDongle-E adapters work great as dedicated Zigbee repeaters / range extenders, best of the best! Another alternative is the Aeotec Range Extender Zi but it is quite expensive so much better getting more of the IKEA Trådfi Signal Repeater for the same budget.