It would not, simply because joining the Euro Area isn't a one time thing, but a series of steps, and they wouldn't move forward as long as the inflation is higher than in the rest of the EU.
> If Iceland adopted the EU's interest rate which is mainly set for France and Germany, that would be a 5% interest rate cut which is a massive stimulus.
Interests rate is only one of the factors involved in controlling inflation, and the fact that Italy has been able to adjust its economic policy in order to align its inflation figures to Maastricht requirements and join the Euro Area is a good proof of that.
> People should also look into Optimal Currency Area theory popularized by Paul Krugman
It has been popularized by Robert Mundell in the 60s, for which he got the Sveriges Riksank prize (the "Nobel") in 1999, not by Paul Krugman.
> For all the above reasons, Iceland joining the EU would be the stupidest and most economically illiterate decision in it's history.
The creation of the Euro is IMHO the "most economically illiterate decision in […] history" but moat of your arguments above miss the mark.