If yes, is it slower than regular questing?
Yes you can - it's perfectly possible to level from PvP. You will get experience from many activities from getting kills to capturing flags but the main source of experience will be from winning. This is especially the case when you're doing a 'Call to Arms' battleground as the experience bonus from winning a call to arms battleground will normally result in a full level or more at low level, and a large portion of a level at high level. This does mean however that queuing for specific battlegrounds will not result in the experience bonuses.
Regarding the speed of experience gain, yes - it is overall slower than questing, since you spend a period of time waiting for the queues and you're not guaranteed a win but if you end up with multiple wins in a row you will gain more experience than any other method of levelling during that period.
Your best bet is to do a mixture of questing while queuing for battlegrounds, although replacing dungeons with battlegrounds is generally more consistent in terms of experience gained.