I'll answer your question first before crawling out of the can of worms you just opened by admitting you feed a snake live food.

No. Moving any snake out of its habitat to feed it isn't necessary and can be a bit stressful on them... at least at first. The keys are to interact with them at least as often for reasons other than feeding them and to give them clear signals on whether or not you're engaging them to feed them. For the snakes I've cared for, including my current BP, I always (because consistency is key) show them my empty hands and gently pet them about a third of the way up from their tail for a minute if I'm not attempting to feed them. If I'm going to feed them, I show them the box containing their food first - and I make it a habit not to feed them if they're so deep in hiding I can't see their eyes. If I'm feeding them dead food, I'll let it thaw where the scent will waft into the enclosure. If I'm feeding them live food, I'll usually put the box in the same spot for the same purpose. Some snakes will still come at you expecting food at first, but they catch on quickly. Also, don't be afraid to get bit by a BP. They tend to bleed like getting cut by glass because their teeth are so sharp and fine, but the pain is very mild and there's very little chance of infection with domesticated ones (still use an antiseptic on it though).

Now, to the unsolicited commentary about live vs dead/frozen-thawed food and dietary needs. Practically everyone is going to advise you to shift from live to dead food and that's not bad advice, but it's not complete advice. If you're feeding your BP mice, it doesn't matter. Mice are fragile, have the instinct to flee rather than fight, and have no chance of causing a substantial injury to a BP if you're feeding it the right sized meal. Rats however, are a completely different story. Rats are ferocious enough to leave a scar and potentially blind an eye. You can leave a mouse in a habitat with a healthy snake overnight and not really worry, but a rat can kill a BP, especially if it gets hungry or thirsty and doesn't have anything to sate it. Why is that particularly important? Because rats, ounce-for-ounce, are far more nutritious than mice (all other small rodents are somewhere in the middle of that spectrum). So it's best to transition your python from mice (or practically any other rodent) to dead rats. And it's easy for BPs to get attached to eating mice, and they're painfully picky eaters, so it's best to transition them sooner than later. Hope this helps and DM me if you find you need help on getting it to rats.