Short answer: NO
Long answer: NO, well on an CD you can't, but as theKbStockpiler mentioned if you have it installed in an USB stick then it is possible, but it isn't the same as having it in the hard drive thou.
Now you can try Tinycore
Linux which runs from LiveCD or USB stick and you can load programs on fly and do things almost as it was installed, there is a way too to make those programs loaded persistent if you are using USB stick, but Tinycore
have way different philosophy of Ubuntu.