Yes, but the House has to pass the Bill FIRST.
No, they can actually pass them in which ever order they like, so long as Obama signs the original legislation first. In other words, they can work out all the problems - in theory - and then have the House pass the original Senate bill. Then, both the Original Senate bill, and the Reconciliation Bill would be sent to Obama for his signature. It's kind of a dirty legislative trick.
And if the House passes the Senate bill first, then its a done deal, with or without any changes via reconciliation.
In fact, at that point, we may want reconciliation to make the horrendous Senate bill more palatable, however slight it may be.