No, you shouldn’t use a free VPN for Team Fortress 2. Free VPN services cannot offer you the security or privacy that the paid providers can, not to mention that free VPNs are notorious for selling user data to third parties.
But as a Team Fortress 2 player, you shouldn’t even want to play with a free VPN. It’ll likely result in connectivity issues and slow speeds because of bandwidth limits or weak infrastructure of the service.