there won't be any down time, because you only changing registrar not changing hosting which in this case include a changing IP which the cause of downtime before dns propagation update.
for the case of changing hosting, if you want no down time at your end, you can use temporary: "xx.xx.xx.xx yourdomain" record on your host file, where xx.xx.xx.xx is your new hosting assigned IP.
i had terrible experience several years ago with 1&1 that i want to share:
1. they have different domain manager back end. find the real one because the regular one on our account do not reflect on that real one. before you transfer your domain, make sure you turn off its auto renewal. because they will still charge you for that domain till kingdom come. i know, they are bastards.
2. if you have other domains on your account, do not cancel your auto payment agreement, because they will just ban your acc instantly and you loose access to your other domains. their support is decent but it's their security team who will screw you and they are god-like bastards there transfer out all your domains or turn off their auto renewal on the REAL hidden domain manager
[edited] i just remember that you must cancel the "contract" too on the real domain manager. so there are two things to cancel, the auto renewal and terminate the individual domain contract. then cancel the payment agreement on your paypal if you use it as your payment method.
