My theory is that all rabbits are scared of heights. I can pick up my Charlie, but he does this little oooomph sound when you lift him like he's saying OH NO, then he'll snuggle, but he breathes quickly and he'd clearly rather not, so I only pick him up when he's being very bad indeed. Also he looks disappointed in me, stamps his feet and doesn't forgive me for at least 2 minutes. Lex doesn't like it much, although he forgives and forgets the instant he's back on the ground again. When you lift him though, he'll try and climb out of your arms onto your shoulder like a mad parrot and then get this look on his face like he's going to launch himself, so I only scoop him up quickly if I have to. He comes when he's called though and follows me about like a puppy, so I never really need to pick him up. And Fudgie... Ah Fudgie... She hates being picked up so much she doesn't even GET scared. She gets angry. Then she gets even. Trying to carry Fudge involves being relentlessly nipped by a furious fat rabbit who won't speak to you for days afterwards. if I carry her, she'll ignore me and run away from me for about a week, so I try really really hard to never pick her up. In return she will pay attention to me about the 15th time when I say, "GO HOME FUDGIE!" in the evening, she will eventually ramble across the garden and get in her hutch.
So no. that's the simple answer, they don't like to be picked up, and chances are they'll whimper, or stress, or run away from you and generally make you feel like a rapist.
However they will come and pester you for love once they trust you. lex chews my shoes if he feels I'm not paying enough attention to him, and he climbed into my lap the other night when I was watching tv. he's a bit of special bun though - I've never had one as friendly as him. Charlie, if I stroke him for long enough, til he's happy and chomping with happiness, will let me curl around him on the floor and cuddle him like a living teddy bear. But Fudgie says I can sod off. No Fudgie cuddles for me. She still loves to be loved though, and will flop out and doze while I pat her.
She'll even lick me sometimes. Lex practically washes me with love, he'll kiss anyone, the big tart, but Charlie will only occassionally give a me a quick lick on the leg and walk off like he's embarrassed and he wishes he hadn't. weird, brilliant little beasts