That seems pretty unlikely. Seattle isn't exactly crawling with illegal immigrants.
Even if it were, would you expect the number of illegal immigrants coming to Seattle was greater over the past 5 years? If so why?
And even if Seattle were some sort of super-secret, great illegal immigrant mecca, why would there be any reason to believe that they would have an impact on housing? Because they're wealthy enough to afford the low end ($300k)?
Judging by the people I've seen in Capitol Hill, I think it's more likely that extra-terrestrial aliens have a bigger impact on Seattle Real Estate than illegal aliens.