The garage is fed from a double pole breaker in the house.
Then there should be 3 wires going to the garage panel: Leg 1 of 120VAC, Leg 2 of 120VAC and neutral; there's 240VAC between Leg 1 and Leg 2, 120VAC between either leg and neutral.
Your router will be on the same side of the panel (same "leg') as one leg of the garage so the PLA could very likely work.
The PLA's don't require being fed by the same breaker but instead most require the 2 PLA's being on the same "leg" of 120/240 (the same side of the panel).