If the immigration bill passes in the House of Representatives, will immigrants be granted citizenship immediately? Why or why not?

No, it would have to follow the entire law-making process to make any effect.

Explanation:

Any law of the Congress that has the purpose of regulating rights in the federal territory must follow a determined process. Thus, any bill that enters one of the two chambers of Congress must be approved by both (the House of Representatives and the Senate) in order to become law. Once approved by both houses of Congress, the bill passes to the President, who must sign and enact it to obtain the force of law. If the president does not sign it for more than 10 days, the bill is considered approved. The same if the president vetoes it but the Congress, by a majority of two thirds in both chambers, re-approves the project.