Seriously, people have ridden 'centuries', across countries, around the world on any/all kinds of bikes.

Your Crosstrail is perfectly fine, in and of itself, including its suspension fork. Here's what matters.

1. You want your bike in good/perfect working order on the day.

2. You might want to consider appropriate tires (i.e. better than stock), but even then, no matter if what's on there is in good condition.

3. That said, by far the most important two things:
a) your bike should fit you properly/you should be very comfortable on it over distance, and
b) you should 'train' a little, even if informally (it really doesn't take much), targeting 'the big day'. Doing so also helps you check 3(a) and 1.

How to do that (3b)? It's really pretty simple. Try to work out a schedule that allows you to do rides of increasing distances, in smallish increments, up to about 2/3 or 3/4 your target distance for 'the day', with that last, long ride a week or 10 days before 'the day'. In other words, if you can comfortably do a ride of 60 to 75 miles in a reasonable (for you) time a week or 10 days before your century ride, you're there. Then taper off, and go do your big ride.

There's no magic in any of this, contrary to what many sources would have you believe. You don't need a special bike, or special modifications to your bike, or 'scientific' training plans, or any other such nonsense. You need a bike in good working order that you are comfortable with, and some reasonable fitness.