Most plasma/LCD have a component option, I would check the owners manual to see if the TV is setup to receive 1080i/p over its component jacks. For the sake of argument lets assume the TV does, it would also depend on the Cable/Satellite box the TV is connected to. There are some Cable and Satellite companies whose boxes don't have 1080i/p support over its component jacks.
If both do then yes you'll get the 1080i/p your TV can display. The argument of digital vs. analog comes into play only if you have a true digital TV. If you were using a DLP projector or HD-ILA etc, you would want to use a digital cable so no converting takes place.