A widget will use up RAM if it's on any of your screens, regardless of which screen you're on, which will potentially slow down your system. Removing the widget from your homescreens will free up that RAM.
To see how much RAM a widget (or any other app) is using look here:
[menu] -> settings -> applications -> running services
Depending on the widget's functions, it may use CPU at different times. e.g.
* All the time it is displayed, e.g. a clock widget with animated second hand. When you switch to a different homescreen, the widget should stop eating CPU.
* Periodically, e.g. an email/twitter/facebook widget might go off to the internet every now and then to check for status updates etc. Ideally you should be able to configure how often it does this - setting the period to once per hour instead of every 5 minutes can save LOADS of CPU and thus battery. Typically this behaviour will occur regardless of whether the widget is currently displayed or not.
* When you use it or interact with it in some way. E.g. status toggles or refresh buttons. CPU/battery use in these situations is typically negligible, unless youre clicking the damn thing every few seconds.
* Conceivably a widget might use CPU all the time regardless of whether it's currently displayed or not, but i cant think of a single good reason why a widget should need to do this. If you have a widget that appears to be doing this, it's probably badly programmed and i suggest you uninstall it.
If you want to find out how much CPU a widget is using, there are system monitor apps on the market to help you do this, e.g:
System Tuner:
https://market.android.com/details?id=ccc71.pmw
OS Monitor:
https://market.android.com/details?id=com.eolwral.osmonitor
(I'm a bit rusty on these, so they may not be the best ones out there, hopefully someone else can make a recommendation).