Am I able to use call13434 if I am already registered with Tele2, Onetel or another carrier selection provider?

Yes, you can. If you normally dial another Indirect Access code before your calls (for example Tele2 or OneTel) you simply omit their code and just dial 13434 or 01 6850850 instead. If you are using a router box (also known as Phone.Pal) you can either unplug the router box or dial 1-2-1 (or whichever override code is provided by your service provider) to bypass your router box followed by call13434.
Should you have chosen to have all your calls automatically routed through another provider (also known as Carrier Pre-Select or CPS) you will still be able to use call13434 as usual. Just sign up and dial 13434 followed by the telephone number to make cheaper calls! Your CPS provider will not charge you for dialling the 13434 code, therefore the 13434 code will not appear on your CPS bill and any calls made using the 13434 code will only be invoiced by Call13434. Only if you use 01 6850850 you might be charged by your operator.