Definitely not. Even though Gohan had affected his heart somewhat, Piccolo still wasn't the type to show mercy against enemies (something he spells out pretty clearly against Gero) and clearly wasn't the type to listen to authority. Sure, Piccolo might be intrigued by the prospect of testing his limits against a strong opponent, but he wouldn't need to with Vegeta when he's already had Goku as his goal and, even after his realisation of his change, he didn't seem to really change heavily in how he felt towards Goku until after his fusion with Nail. I doubt even someone far more tepid than him such as Tenshinhan would've listened here, considering Goku's best friend was barely able to listen to his demand.