How effective would Alchemy be if I was to use it...but not take archery?

very, though adding poisons to both weapons if you use two weapons is a pain (poison only goes on the right hand weapon, it will not poison the off hand even if the main is poisoned)

Alchemy is useful for all types of builds

Thanks, so I would be ok if I took alchemy but didn't use archery?

Yep. alchemy is always useful even without archery.

I've used it with an orc... always slapping poisons on his greatswords for that extra bit of damage (and paralysis..)