If you're talking about the screws on the front mech, then no, they don't affect the gear cable tension, they adjust the amount of travel the dérailleur has. A slight worry now is that if you've done 2 complete turns and it hasn't worked, you might have adjusted the inner limit instead of making the outer limit a wee bit wider. Before you try the bike out in anger, make sure you haven't adjusted it so that the dérailleur doesn't bury itself in your spokes on the first hill you come across. If that's what's happened, put it back where it was and give the other screw a quarter turn at the most to see if it cures it or, at least improves it. If it improves it, continue adjusting it but very, very gently.
Cautionary tale: I once bought a second hand bike in Sheffield. One mile into my journey home, I found myself needing to accelerate on a steep hill because of a lorry bearing down on me. Luckily the lorry missed me but the bike never went another inch with me on it - the dérailleur went into the rear wheel, wrecking the wheel, dérailleur and knocking the steel frame completely out of shape. It simply hadn't occurred to me that the bike was badly adjusted.