Well, not necessarily. That depends on the ISP. For example, one of the major ISPs (telephone company) in my country use the following approachs for DSL connections:

Customers are assigned 5 private IPs each starting 10.... which are static numbers for as long as you will be a customer and allow access to telephone company's private network. Then the customer connects to "dial" proxy where you actually choose the ISP connection for which you have signed on to access the internet. Upon that time your connection will be routed through NAT proxy and the only way to get your dynamic public IP is to connect somewhere and check where you're connecting from.

For that purpose www.grc.com is probably the easiest for average user.

Your NIC will always be configured on the static IPs assigned to you and since you do not have access to the ISP's routers etc there is no way of knowing your IP unless you use some external method to acquire it.

B Rgds,
Maccara