Have one. Currently shoot 140gr AMAX out the short little barrel at about 2450 fps.
If I load the 140gr AMAX to the lands, there is not enough bullet left in the neck. That's COAL of 3.14" give or take a few thou. Looking at a loaded round in the magazine right now, I think one could get out to about 3.33" That's still using the magazine. Judging from my Hornady OAL guage which I pulled out to remind me where the lands are on my Tikka, I don't think you can load longer than 3.33" COAL anyhow, before you jamb into the rifling....
So if you had a long enough bullet, you could seat to the lands. What's more, the Tikka is NOT a short action, so you will have no trouble ejecting a loaded round.
The 6.5x55 military round originally was a 160gr round nose that was a VERY long bullet. This is also why swedes (and perhaps ever thereafter all 6.5s) are built with a fast twist to stabilize long heavy bullets.
Since those old long round noses are theoretically still out there, especially in Europe, Tikka probably put a generous throat in there (but many factory guns are long throated anymore)...
I picked up my Tikka from a hunting buddy who did not reload and was sick of paying through the nose for cartridges. It shoots about 1.5" with factory loads. I have it at around .5 MOA if I do my part with my 140gr Amax load. I paid $600 and that included a cheap Nikon scope. But I knew it was not shot out, and I knew that some of the accuracy limitations he complained of were the shooter and not the gun (did not tell him that!!)
Go for it!!! But be aware that as much as you might get long range accuracy out of it, I think the barrel length and subsequent price you will pay in velocity limits it. I have my click chart out to 400 yards and I fear that much beyond that, the drops will be so severe that even a minor error in range estimation or wind will result in a wounded animal....