The invasion was going to happen, America was spoiling for a fight even if it wasn't related to 9-11, plus they were too far along militarily to go back. Remember the Bush & Blair Administration were willing to lie to their people in order to obtain "evidence", even when Saddam was disarming his missiles they were still spoiling for a fight.
I can't see the Bush buddies being influenced by the lack of Saddam, this will be used as an excuse to stay in Iraq longer but it'll also hurt the Bush Administration's prestige a bit. There will still be the chaotic American occupation but Saddam won't be able to return to power like the first Gulf War, too many institutions replaced/destroyed.
Like OTL the invasion was still suffering plenty of faults in planning let alone execution.
- There was no credible exist strategy
- It was still planned that the Iraqi army would be disbanded
- No plan for the disbanded army, in fact it may be worse since the possibly of Saddam coming back and influencing the army exists.
- Incredibly slow restoration to normal life in terms of power, water, security, and so on... (still ongoing)
- Poor military administration
- Refusal to let the democratic government in exile take over, instead they choose a puppet counsel based on ethnicity alone.
- Use of trigger happy mercenaries who were given full legal immunity free from military oversight.
- Lack of will to fully commit militarily or economically.
Reminds me of this parody by MAD
http://www.youtube.com/watch?v=xcjLEwZqcQI