You should. They're constantly impressed with the quantity of their applicants that they will only reply to you if they want to hire you at all. Otherwise, you'll spend another six months waiting for an email that will never come.

Try doing that with a startup whose bulk of development is done overseas. No personal work connection, lack of meaningful discussion (due to time zones and cultural/philosophy barrier), no concern for your growth as an individual. You are more likely to be distant from your workers due to startups' smaller budgets discouraging the use of in-house developers.