Having been a regular competitor at USDC with plenty of success, I can speak to more recent years. Personally my first USDC was my 4th competition, very early on in my pro-am experience, I went in with zero expectations, and made a big final or two, a podium placement, and walked away over the moon. If you go in wanting a title, prepare to be disappointed, simple statistics alone, only one person can win per event, afterall. That being said, it is a must do competition for any serious pro-am dancer in the US at least once. When you bite the bullet to go is up to you. My opinion is: the earlier, the better. You'll experience the best of Pro-Am dancing in the country, and that alone will set the tone for the standard of quality you desire for yourself.
The Leaders Only categories will vary in size depending on style and level, but I've had a semifinal or two of only leaders, which is really a great experience. Leaders Only categories in the older age categories regularly have semifinals, even at regional comps, at least the ones that host one of the Leaders Only Tours. If you are there at USDC, you might as well enter the equivalent all gender multi-dances, you never know where you may land, and it is a useful experience to share the floor with professional leader's, regardless of who they are partnering. Nationals is always going to be competitive, everyone there is aiming to be at their absolute best, perceiving it as cutthroat is up to you. There are always plenty of friendly people on and off the floor to make it less daunting. Your fellow gentlemen competitors aren't a shy group, we are easy to talk to, and you'll probably find it nearly impossible to be on deck without some sort of chit chat to break the tension before walking on the floor.
As to Warren's suggestion of finding a top pro.....
All of my competitive USDC years were with teachers that were Rising Star level professionals, but good dancers, and good partners. We worked consistently, and developed a connected, well partnered product. Did I dance with world class champions, not necessarily, but it didn't prevent me from making multiple podium placements from quarters and semis, and winning a couple Gent's titles as well. Good teachers, good dancing and quality partnering/mechanics/musicianship can come from anywhere (think Ratatouille wisdom). No one on here can tell you where you are likely to place without seeing you dance, and even then, it doesn't matter. Any major comp will be subject to great highs, or great lows and frankly, you never know what you'll get and how you will handle it until you experience it. But don't break something that isn't necessarily broken just to find an expensive top champion pro who still will not guarantee you any placement. That is not a trick that works. Also there have been plenty of Pro-Am champions in the past years that dance with pros that don't have major Open Finalist careers results.
If you want basically a guaranteed leader's only event with tons of competition, dance American Smooth at Beach Bash's Supreme Leader event. All ages and levels, and they've had at least a Quarterfinal ever year since the first time they offered it. I've done it twice and have had an absolute blast both times. Also the comp is insanely goofy fun all week for any style, will never feel cutthroat.