this house allow independent candidates to join the presidential election

If we are talking about the United States then are they not already? Certainly third party candidates are allowed; remember the campaigns of Ralph Nader.

On the general question then the answer I think has to be yes; it is not very democratic to restrict government to being by parties (even if it is possible to easily register as a party) as in some cases it may be best to have someone who is completely independent who is not held back by ideology and party politics or not tainted by previous administrations. While the Italians did not elect Mario Monti his is pretty much fulfilling this role as an independent who is just there to solve a crisis.