I am betting you are talking a DSL connection. If it is a cable modem then it will have no issues other than make sure you power everything off so the cable modem forgets any locked mac address.
DSL is another story. In almost all cases the DSL is actually a router. You can put a router behind a router but it makes things more complex and generally does not give you much advantage. You might be able to set the dsl device into bridge mode but then you must configure something like PPPoE in your main router. The exact configuration is going to depend on your ISP. Most time you are going to need some form of userid and password. If you happen to have the rare modem only dsl device then this is the same as running a dsl router in...