yes you can. Depending on which manufacturer has made the key head you may be able to just pop you transponder into a lot inside the key head without having to take it apart.
If you have the key split it into it's 2 halves ignore the remote half & look at the part of the key head where the remote slots onto. If you can see the new transponder sat in a slot in the key head then just whip it out & put yours in.
If you can see it then you need to open the key head up. Under the Seat
badge there's a little screw. Undo that then pry open the key head. Be careful as the spring for the blade can shoot off.
If you've bought it from ebay then chances are there's be an easy access slot for the transponder
As for the remote, yes it's quite straight forward top do yourself with 2 keys. However i never do the manual procedure as it's not 100% successful. Usually i'm programming a full new key so once i've programmed the new transponder I just program the remote straight after with either VCDS or my key programmer depending which i'm using