In some contexts you could use "do" with archery, but not the example you give. As doji said above, you can also use "to practice" with archery, when you are actually practicing archery (practice in the wordreference definition, v 10. to perform on or do repeatedly in order to gain skill or ability).
Here's some examples of context for "do" with archery:
Quotation example 2 (Lawrence) Top 10 Archery Quotes "I've done archery for about six weeks, and rock climbing, tree climbing - and combat, running and vaulting."
From an interview with James Cameron about directing the movie Avatar: "So everybody [in the troupe who played background Navi characters] learned to be Navi and move like the Navi at all times. They did archery, they did horseback riding."
Not in all contexts, bennymix, but in some, sure. For example, my son's friend went to classes in medieval martial arts when he was in middle school. I would not be surprised if he had said that to me when we were discussing that topic (although I would have expected contractions, so, "I'll do archery when I'm in high school.")