Compared to "dedicated" or "purpose-built" .223 Rem F-TR rifles, the honest answer is that you may be at some disadvantage. Unless you have had it re-barreled, the original Tikka setup will have a shorter barrel, a slower twist rate, and potentially less freebore for loading the 88-90+ gr bullets than rifles generally favored by F-TR shooters when using a .223 Rem. A typical dedicated F-TR setup might have a 30" barrel, throated long specifically for 88/90/95 gr .224 bullets. You might be able to load the Tikka with something like a Berger 80 gr offering, or perhaps even the 75 or 80 gr ELDM, but even the 85.5 gr Berger Hybrids would probably not work too well. The challenge with using lighter bullets would simply be more wind deflection under any given set of conditions.
That's the bad news. Here's the good news...who cares? Take what you have, particpate in a match, and have some fun. Tikka rifles can shoot very, very well. Sure, you'd probably be giving up a fair bit of windage to those using much heavier .224" or .308" cal bullets, but it might not be as bad as it sounds from 300 to 600 yd. With your background in service rifle, you might fare pretty well as the only difference/disadvantage would be one of wind deflection, and having the better wind reading skills can largely overcome that deficit. Plus, I would never advise anyone to expect to win their first few times out anyhow, even with the best possible equipment money can buy. There is usually a learning curve associated with any new endeavor. But making the decision to participate with whatever setup you have is the first step. After that, it is meeting new like-minded folks and having fun that keeps you coming back. Equipment can always be upgraded down the road if you enjoy yourself and want to keep coming back. My suggestion would be to run whatever you have to the best of your ability, learn a little bit, and take the rest as it comes. IMO - you're never too old to start something new and have fun with it.