The active gem Blood Rage drains a small % of your max hp as Chaos Damage per second depending on gem level. Is it possible to cancel out/negate that drain with enough life regeneration?
Yes, with 4% HP regen per second, it is very possible to out-regen the chaos damage.
When you get into Cruel and Merciless modes though, you start with -20% and -60% chaos resistance though, so (without chaos resistance) you'll be taking more than 4% HP damage per second.
One way to deal with this is to get Chaos Resistance, but Chaos Resistance is rare and hard to roll on gear (ie. Expensive to get). You can also just get additional %regen to compensate further for the extra damage you are taking. Additional Regen can be obtained throughout the passive tree, through Vitality Aura gem (gives close to 2%) or through certain unique items.
Blood Rage gives you Frenzy Charges, so one of the best items to get to out-regen it is Blood Dance http://pathofexile.gamepedia.com/The_Blood_Dance
These boots will add 1% regen per frenzy charge you have, so you can get 3% regen just by having 3 frenzy charges, which you will almost always have since you get a frenzy charge on kill while Blood Rage is active. You can get up to 7 frenzy charges by passive tree (3) and Act2 Bandits Quest (in Merciless mode, help Kraityn)
Edit: Since the introduction of corrupted items, it is possible to get more than 7 frenzy charges, since you can corrupt certain items (including The Blood Dance) to give +1 frenzy charges as the implicit stat.