ACCESS_FINE_LOCATION permissions can't turn on and access location services if they are disabled (assuming your phone isn't rooted). However, the app could still try to enable location services or find your location with other methods.
Vulnerabilities have existed to turn on location services without user interaction, however there is no intentional way to enable GPS programmatically without user interaction.
Without allowing the location permission, apps can still see your external IP address and router BSSID. Your IP address can be used to
try to find your location which will probably only be accurate to the city / region (iplocation.com).
Your router's BSSID could be used to find a more accurate location if somebody has used a wardriving service like Wigle to map out your WiFi network location on Wigle's global map. This would allow the app to enter your BSSID into Wigle's API and find a precise location. If you were to have enabled location services, the app could gather BSSID addresses of networks around you for a more accurate location.