Will the drop counter reset if I craft a badge?

I'll explain this in two parts:

The Green box highlights a F2P game utilizing a Micro-Transaction model. As you can see, it says "no card drops remaining". But I can get more if I purchase any item from the store in increments of $9.00 (ie I spend $18.00, I get 2 cards). Thus, for games like TF2, you don't necessarily have to trade to get a badge Lvl2+ (but is advisable).

If you look at the red box, however, since Bit.Trip Runner2 is a paid game, it features a permanent drop counter. Meaning, once the 3 card drops I have left are given, there will be no more card drops, by playing the game. Once you've received all possible card drops, you may receive a booster pack, which contains 3 cards, either basic or foil. The rate at which these booster packs appear in your inventory depends on your steam level and as game badges are crafted by the community. Keep this in mind if you plan to sell or trade those cards out.

Associated question: How do trading card booster packs drop?

Unfortunately, the drop counter never resets.

You can increase it in F2P games at the rate of one card per $9 though, and when other people craft badges there's a chance that you can get a booster pack containing three card, it being more likely the higher level you are.

The main way you'll have to do it though is to buy them from people or farm them with alt accounts.