There are no official sources for Vegeta's powerlevel at this point but imo he should be a decent amount stronger than Piccolo as Piccolo was shocked to see his powerlevel and Vegeta was unafraid to fight Frieza in his final form, something Piccolo didn't do. Also when Goku arived it was clear that he was the strongest Z Fighter there and acording to official readings his pl was 3 million when he first fought Frieza and Frieza himself was at 6 million. So i think Vegeta was around the 2 million range so he should have little problem defeating Frieza in his second form who is a little over 1 million.
There is a distinct lack of information as to how much Vegeta actually powered up due to Krillin's blast, if any at all. Final Frieza was only toying with the saiyan, and no new feats for Vegeta were ever revealed. So just like @Justalittlegirl: said, this match seems inconclusive.
But I think if Vegeta (Who had already been in fear of Frieza's first transformation when Frieza first did it) did do this plan then he wouldn't bother giving Frieza the chance to power up further. I think if Vegeta dominated Frieza, then that might actually work better. If Frieza looks dominated then I think Vegeta wouldn't want that to change in any way. So he wouldn't bother with his own ego in favor of the sight he always wanted to see. Frieza down on his knees in front of him.