From my favorite armchair general's opinion (me).
20K is not enough to effect the problem in the whole country. It could have a localized effect in certain areas, but many insurgents would just end up squirting to another AO. We would end playing "whack-a-mole" throughout the entire country.
Hindsight being 20-20, we should have kept max numbers of troops in Iraq from the beginning. Think Clear-Hold-Build.
Personally I think the only way to pull it off is max out the number of folks in country, cut off the PC bullshit, clear out the media, and systematically clear out the country. It will take MUCH longer doing that now, versus 4 years ago. To completely do the job now, we'd have to sit in country for at least 10 or more years. Obviously this can be affected by how long it takes to get decent, not corrupt IA/IP units operating.