If you have been using spot metering extensively, you likely already have a very good sense of how to read the light in a scene--you know how to spot extremes of light and shadow and you have a good sense of what sort of dynamic range your film will handle. That experience should help you in identifying which shots will be troublesome for your center weighted meter.
Since a center weighted meter takes an average reading of the light reflected from the center of the scene, it is based on the assumption that most scenes that you want to photograph will average out to be medium gray. Since that isn't always true, a decent gray card can be a big help--you should definitely take one and use it. Since the gray card presents the meter with exactly the sort of gray scene it is best designed to handle, it allows your meter to measure the light falling on the scene independently of the reflectance of the particular subject -- the camera's meter in effect becomes an incident light meter (assuming the gray card is properly positioned).
There is always a learning curve with any new equipment, so the more time you can take to practice, the better your results will be. I'd suggest making careful notes of your exposures, particularly for the first few rolls, bracket liberally, and process your film promptly so you get immediate feedback.
