Josh put it pretty well.
You definitely have the ability to hang in fast races. Training for cycling is initially a matter of time and patience, in re-teaching the muscles to do something different. It takes varying amounts of time to come around from person to person. One rule of thumb I heard when I started was that it takes 2 years of conditioning the leg muscles to really understand the demands of cycling. That's not saying you won't be competitive for 2 years. You may have Cat 1 potential, and be ready to race with Cat 4's after 6 months.
Josh made a great point about bike handling. This cannot be under-emphasized. Riding even in Cat 4 races, you will hit speeds you probably cannot maintain alone. It will require getting comfortable riding very close to other riders, at high speeds, on technical courses. This way, you maximize the aerodynamic advantage of being in the group. The most successful riders in any field have mastered this ability, and will put forth very little effort for 90% of a race, and inflict major damage late in the race (when it counts!).
As far as your follow-up question....training requirements depend on lots of things. The first, your natural ability. You'll discover where this gets you over time. Also, what are your goals in racing? The training demands for being able to hang in the field vs. racing to win are very different. I know guys that train 4 days a week, 1-3 hours per ride, 5-8 hours per week, that are very competitive in Cat 3 races.
Personally, I trained 8-15 hours per week last year, which was my first year of serious racing. I began the season as a Cat 3 (yeah, getting approved for a Cat 3 upgrade is fairly subjective). However, I justified my Cat 3 status, and had 5-6 top 5 finishes, including one win, and the overall win for the state's season long series. This year I upgraded to Cat 2, but reduced the training time, due to family demands (7-11 hours per week). I still have no problem hanging in the field, and even got in the winning breakaway in the state road race.
Although I trained less this year, I trained more specifically. I picked up a power meter, and added structure to every single workout. I used a periodized approach with a base phase, general preparation phase, and race specific phase. However, power meters are expensive, and quality training can happen in other ways. A good general rule-of-thumb is to do lots of long, slow stuff in the winter. Incorporate some tempo and try to get into a group ride once every 1 to 2 weeks.
In March, start to mix in some higher intensity stuff. Most group rides will start to spice up this time of year, so they can be a good place to get this done. Throughout the year, it is good to do one long ride per week. Typically 3 to 5 hours. Obviously, you won't want to jump immediately into 5 hour rides. Give yourself some time to get comfortable on the bike.
Once you get into the racing time of year, you can use the races themselves as good training. In my area I have the
opportunity to race 2-3 times per week. If these are short (45 min to 75 min), you won't need much recovery time afterward and can usually race hard or workout hard after 1 day recovery (often even the next day).
Cycling, as with running, depends alot on how many miles you can put in. If you have a ton of time to train, use it. I know guys that absolutely sucked one year, but had schedules that allowed them to train a ton. They rode 3-4 hours a day, and ended up competitive in Cat 2 fields within a year.
Bottom line, you can be successful in the Cat 3, Cat 4 levels with pretty wide ranges of training commitment.