Not with a LaRue, and not sure I would since they are high dollar rifles made to shoot those calibers, but you could do either one without a problem that I can see, except for maybe mags for the 6.5 and maybe a bolt, but not necessary. If you haven't purchased the LaRue yet I would recommend the LMT as it has the ability to quick change barrels into numerous calibers including the .260. They are also excellent rifles that are accurate and very well made. EVen the British Military thought so because they use the LMT in .308 for their DMR rifles. Sorry to ramble a bit just really enjoy the AR or MSR if you will and have much experience with it. I have been looking into an Alexander Arms 6.5 Grendel as he is the best on that caliber. But yes you can switch the barrels on either rifle. If you talk to LaRue they may even help you out. Their customer service is great and the owner will speak with you as well if needed.
Larue just started offering separate barrels for their rifle. Still only available in 308 or 223. They offer from 14.5 to 20 inch in the 308. Supposedly they will eventually offer barrels for some other cartridges.