Pretty sure that's a no for combat use – T-Lentor 2 (under its various designations) still had several Gamecocks in '39-'40, but it was their advanced fighter training unit. From a sadly now-gone Geocities site on Finnish fighter training:
Gloster Gamecock IIGA-43
Damaged in forced landing before the Winter War on 20.10.1939. Sgt N. Satomaa was not injured.
Plane was removed from FAF inventory in 1941.
GA-44
Damaged in forced landing before the Winter War on 20.10.1939. Cpl M. Aalto was injured.
Plane was removed from FAF inventory in 1939.
GA-45
On 24.2.1940 stalled and damaged. Cpl R. Liikola was not injured.
Plane was removed from FAF inventory in 1940.
GA-46
On 13.12.1939 damaged slightly in a collision with another plane at Parola airfield (pilot Cpl J. Dahl).
On 18.12.1939 "ran away" prior to take-off and damaged. Cpl H. Ketola was not injured.
On 31.1.1940 plane was relieved to State Aircraft Factory (VL) for repairs.
GA-49
On 11.12.1939 crashed and destroyed completely at Parola airfield during firing exercise.
Cpl (Res.) V. Snellman was killed.
GA-50
On 12.1.1940 landed at too slow speed. Plane was slightly damaged, pilot Sgt L. Lehtonen was not injured.
On 12.1.1940 plane was relieved to State Aircraft Factory (VL) for repairs.
GA-55
No damages during the Winter War.
GA-58
On 10.3.1940 crashed in a spin probably after flying in formation at too slow speed with another GA at 50 m high.
2Lt. P. Linnala was seriously injured and died on 13.3.1940.