Short answer, yes.
Bighorn has done a great job of holding machining tolerances to the point that the TL3 actions are well within 0.001 of each other, and from what I've heard from gunsmiths more realistically within 0.0005. I don't know if they can guarantee that ALL of them will be exactly the same or that Bighorn endorses this approach, but from a practical perspective I've got a high level of confidence in the action to action consistency.
I've got a pair of TL-3's that headspace and time (engraving location) exactly the same. I have a couple PVA barrels which were chambered based on only having one out of my two TL-3's in hand, but both barrels work perfectly on either action. I have another couple barrels from a different gunsmith that were chambered off the spec of someone elses's TL3 that he'd had in the shop. Just talked to him about it in advance, went over the specifics, and since he'd had several TL3's in hand that were all pretty much identical he just chambered the barrel to match those never having had my action in hand. The headspace on my barrels was perfect, and the engraving timing even lines up in the correct location too. Now obviously this is a non-traditional approach and if things didn't match perfectly that was on me not on the gunsmith, but it worked out great. I recently bought a used barrel from another shooter who had a 7SAUM chambered by a different gunsmith for his TL3. Again, the barrel fit perfectly, headspaced exactly the same on my action and the engraving lined up in the exact same spot. Another incidental story... had a fining pin break on my TL3 and discovered it at a match. Pulled the bolt out of a buddy's TL3 and swapped it back and forth between his action and my action shooting the entire match. Worked perfectly and when I got home the fired brass was exactly in spec same as my normal measurements - headspace matched perfectly.
I'd have no hesitation swapping barrels between actions or buying a second hand barrel from another TL3 action. Obviously you want to check things as you go along, but in my experience the TL3 seems to be plug and play.