I have not tried to connect it to the Swisscom router but from memory the "centro grande" does not contain a DECT server as the "box-plus" does.
As long as the router has a DECT server, it should be able to connect to all DECT phones.

I have this phone with the Swisscom Centro Grande modem and the Fritzbox 7490 router. Everything works perfectly. I have my contacts from Gmail, but there is just currently a bug because Google has changed the structure of the Gmail API and Friztbox has to update. I just use the Centro to pass the internet to the router and phone.

I strongly advise against buying this phone if it is to be used with a Swisscom internet-box. The phone is well recognized in DECT but there is no functional application without having the Fritz!box. It is impossible to access the address book or to save a contact.