The timer on the potion starts as soon as you quaff it and if you don't finish the enchantment, including naming it and hit the Craft Key before the timer is up, then the potion will have no effect.
I had a real problem with this. I thought the same thing, at first. I realized the timer kept running, so I just done everything as soon as possible.
But, I later realized (on the Xbox, I have yet to try this on the PC) that as long as you get the gem, enchantment and the item selected, you can take as long as you want with the name.
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As far as the effect pots have on the enchanting...I assumed it was like Smithing and only increased the effectiveness of the item, once you passed a certaqin skill level. However, I do think it actually increases the amount of uses you get from the item on a gradual "per skill point" level.
There is a lot of info on the WIKI, but it is too confusing for me to follow, without a tutor.