Yeah pretty much. Considering killing the fiance didn't exactly change the outcome of what Light was trying to do in the first place I think the author could have let Light fail in trying to convince her. At least it would show that Light can't always win at every situation.
If he failed to convince Misora, she'd lead the investigation towards him. She'd just look into the last person he was tracking, and bam, Light is cornered.
It probably wouldn't have been 100% damning, but it's something he really didn't need to deal with.
@Natty:
Not to defend anyone, but if she was such a great detective, she could have suspected Light of lying. Instead of believing everything he said.
She didn't suspect him of lying, but like I've said at least 90293750923750923 times in the past page or two, she pretty much refused to give him the time of day for most of his conversation with her. She kept saying:
"No, I think it'd be best if I really do go meet with L."
"That's nice of you, but I really must be going."
It was obvious she didn't really trust him. Or anybody.
Not to mention L suspecting Light even more while watching the camera's didn't make a lot of sense either. "Hmmm Light is doing what every other normal teenager does! That must mean he's Kira!"
He grew suspicious because Light was too perfect of a student and teenager.
All Light ever did is go to school, study, eat, and sleep. That's it. L looked at that and thought that it might be a ploy, even though that's all Light ever really did do. Normal teenagers do more than that, even highly intelligent ones, so L thought it was suspicious that Light "seemed so innocent."