Quote from sle:
Well, your exposure is forward vol (you are long root-time vega, unlike in a calendar), so the main exposure is the overall level of vol. The slope of the term structure is going to be influencing the level of the specific forward vol, but unless you are trading an event in single stock, you are mainly exposed to the overall level of the implied vol.
While it sounds like a great deal, it's not necessarily so - when overall level of vol is low, the term structure is steep and you are buying forward vol at a higher level and rolling down to spot. When the term structure is flat, the roll-up is in your favour, but you are usually buying forward vol at a pretty high level.