Queen's stamina, by hype alone, should be above Jack's, who has huge feats, and so should his resilience, which means Pica in that regard is screwed. I don't see Pica being strong enough to injure Queen even if he's in his giant statue form. In fact, if they were to clash attacks, I see Pica's statue losing limbs.
Consider that the Zoro that's in the current fight on Onigashima is stronger than he was when he demolished Pica, and Queen, even if weaker than Zoro, is already handling his attacks better. Back then, Pica's haki was already totally helpless against Zoro's. Queen's physical feats on Big Mom are pretty solid too and he still has cybory things and swordsmanship left to show off.
And now that I think about it, most importantly: are we also taking into account Queen's biological weapons? They're part of his arsenal after all and Pica doesn't have Chopper around to heal him from whatever Queen has cooked up.
I see Pica being capable of surviving a match against Queen by running away in due time, but not defeating Queen. Meanwhile, I don't see Queen needing to run away to survive the encounter.