Yes, with the correct NAT settings you don't need the patch. As long as for the server it looks like everyone is connecting from a local IP, everything is fine.
For the server, you don't need any change in the woncom.lst for the BetaStrike server list. Once you register your server on the website, it is checked by the master server and doesn't need to update itself. I have never used the "steamless" project, because it is for newer HL version (1.1), which are not compatible with the old CS Betas 5.2 & 6.1.
For your client, I don't think you can "merge" them in any usable manner. You can list more than one server in the woncom.lst, but your client will only pick one at random and connect to that one. It will not connect to all of them and show all results. So you have to choose which servers you want to display.
Yes, there is an old admin mod version that works with HL 1.0.1.6 and CS 5.2/6.1. I'm using it on my servers. Check the downloads section, this is the newest version of admin mod that sill works with the old HL protocol:
http://www.betastrike.net/downloads/server/admin%20mod/One remark: Please note that in the CS Beta community we have changed the mod folder of Counter-Strike! So please don't use a "cstrike" folder name. This was done so you can use one HL installation and easily switch between CS 5.2 and CS 6.1. The folders should be named "cstrk52" or "cstrk61" etc..
To make admin-mod work with this change, simply open the admin-mod .dll/.so with a Hex-editor and replace "cstrike" with "cstrk52" or "cstrk61". CS itself will run without any modification with the changed folder name.