Heal Spell and Damage Overflow, Does a Heal Spell stop you from bleeding Options

[bit_buckethead]

Here is a question that came up last game. Does a heal spell stop you from taking more damage if it leaves you still in damage overflow. Here is the situation:

The street sammie got into an argument with troll with a LMG. To make a long story short the sammie took 15 points of damage from the argument. The sammie is still alive because he has a body of 7. Now the team didn't have the people to leave behind to biotech him until they could get him to a doc, nor could they carry him with them on the rest of the run. They figured that they would leave him there and pick him up on the way out. So the mage cast a heal on him and got three successes. Giving him back 3 points. They then left him to complete the run. Now for the questions.

1. Does the street sammie continue to bleed out while the spell is being cast? Or does the spell stop the damage from accumulating while casting?
2. Does the heal spell, when complete, stabilize the character? If not, does the character still get a chance to self-stabilize?