Yes each tag added from the Marketplace in TIQ has it's own template file. So, you can create two instance of any tag, distinguish them using separate load rules if necessary, and as you mention, modify one of the tag templates to support Header Bidding.
Here is a reference to an article discussing how to edit tag templates:
We recommend that you save a backup copy of the template (as mentioned within the article above). Also, we recommend that you use the Save Profile Template option.