My experience - the T3's will shoot. I agree with an earlier poster who said you need to experiment around any "good load"(s) that you may have had in 'other' 243(s), because this one won't be the same. Two in a row from the same production line likely won't be the same, so get 'the load' right first - as good as you can possibly get it to be, in your specific rifle. Then go from there.
Actually, I will normally do barrel break-in with factory ammo, or a range of factory ammo's first- saving my brass as I go.
(If I find something truly amazing... consistent, repeatedly amazing, well - I might be close to being done!)
Once broken in good, I baseline it - shoot some 5-shot groups and save those back for comparison later.
Then if not satisfied, or I just decide to tinker later, I usually adjust my triggers first and get that out of the way.
Test again to make sure I'm moving it in the right direction, am still safe, etc., repeating as necessary.
Then do some load development work, establishing the best load for the specific rifle.
Then if still not there, I'll mess with it some more!
(I don't care what they say about their tupperware stocks, mine shot better after sanding for a very complete float ALL the way back.)
But like somebody else said, do go slow on barrel floating work especially.
Test again to make sure you are improving things, repeating as necessary.
I had one heck of a time getting my T3 Lite in 243win to shoot, but we're there now and it is sweet! One of my favorite rifles, no question.
I worked with another Tikka T3 SS in 30-06. Trigger first, and excellent (both Tikka's are, after really very minor adjustments).
A little bit of sanding, but nowhere near as much as my 243. The stock still has one pressure point near the very back.
Lots of good load development work, and it is throwing groups with 180 Nosler Partitions now that resemble what I can do with my 243 with 70NBT's which to me is pretty incredible.
Make sure you are cleaning it good in between test sessions, giving it a couple of fouler shots (my 'settling into the bags good time'') before trying to shoot for groups at the beginning of each new session, and don't let your barrel get too hot.
Best of luck to you and if you need any recipes that worked in mine (no guarantee for yours), just shoot me a PM.