Yes, it's pretty definite that Jean killed Scott. She never comes right out and says it, since her Dark Phoenix persona remains dominant for most of the movie, but there are several lines of dialogue that make it clear that's what happened.
Jean almost admits what she did in the exchange with Logan, when she returns to the X Mansion. Dark Phoenix Jean starts to come on to him very strongly, but when he backs off, she seems to "regain her senses", followed by this dialogue:
LOGAN: Where's Scott? Jean?
JEAN: Where am I?
LOGAN: You're in the mansion. You need to tell me what happened to Scott. Jean, tell me what happened to him.
JEAN: Oh, God.
LOGAN: Look at me. Stay with me. Talk to me. Look at me. Look at me.
JEAN: No... (starts to weep) Kill me.
JEAN: Kill me before I kill someone else.
Right after this, Jean seems to return to her Dark Phoenix state and leaves. Xavier then finds Logan and, who says:
ORORO: What happened?
CHARLES: What have you done?
LOGAN: I think she killed Scott.
Later, when Xavier tracks Jean down at the house, and tries to convince her to get help controlling her power, one of the things he says is:
CHARLES: Trust me. You're a danger to everyone. But I can help you.
ERIC: I think you want to give her the cure.
XAVIER: Look at Scott. You killed the man you loved because you couldn't control your power.
JEAN: No! Stop it!
Admittedly she's in a bad condition at this point, but she doesn't seem to be denying the act so much as trying to get Charles to stop talking about it, and stop trying to "get in her head".
On a closely related note, the events of this movie were essentially erased from the timeline by X-Men: Days of Future Past. The ending of that movie shows both Jean and Scott alive and well at the X Mansion, and apparently happily together as a couple.