Yes. Logic has these features. The basis of taking many takes, and 'punch in' recording is a basic concept in a recording studio. All pro DAWs have this feature, and have for a long time.
In Logic Pro if you want to punch in, just make sure Audio>Punch On The Fly is enabled.
You can set the 'take' length with the
Autodrop zone, which marks the beginning and end of your recording spot.
Logic automatically retains ALL audio and takes from ANY operation. It never overwrites anything. When you are done you can then simply open the Audio window and remove takes or audio files you do not need, or switch to an earlier take later.
Read up on Autodrop and the Record Toggle command in the manual.
And you can do many things with the form in Logic like the 'arrangements' feature in GB. See my above post for two examples.
Check out these forums which have good info on Logic to get you started:
http://www.bigbluelounge.com/forums/index.php
http://discussions.apple.com
http://logicprohelp.com/
http://logic-users.org/
There are many book and DVD sources with more on Logic if you need more help. I highly suggest the Sitter book.
Logic can do lots of stuff, but it takes awhile to find everything in there. I too, had the initial 'where is everything?!' shock when I first started using Logic.