Yes you can use linen in machines for all stitching applications it's the premium thread for leather use how ever linen has no elasticity or plasticity, it will not give, nylon on the other hand is at the other extreme high elasticity and plasticity which makes it virtually idiot proof it's also the lowest quality thread. Because of its complete lack of forgiveness accurate machine setting essential and quality components especially in the thread path also recommend and you don't need as much tension with linen as it holds a much tighter stitch than poly threads. Needle and awl machines are only of benefit on very hard leather otherwise Pearson's are much better and these useless for your application, thread treatment isn't needed for your application either, if you do use them regular cleaning is a must I do my machines once a week everywhere the treated thread runs must be cleaned the longer you leave it the harder it is to remove and a wax pot needs a good thread wiper and shuttle bobbins must be used the day they are wound. Barbour's and Somac I use both and are excellent machine thread polished linen can be problematic in some machines so best stick to satin finish, I usually buy my thread from Abbey Saddlery, you could get in touch Coats or Somac and ask for local suppliers, http://www.somac.co.uk/linen_thread.html http://www.coatsindustrial.com/en/products-applications/industrial-threads/barbours-linen
Here's a video of Hermes watch bands, this process is what's called hand stitched ends and bends on a regular medium weight closed eye sewing machine (Pfaff 335)with dry Barbour's linen thread looks like 25/3 this outlasts hand stitch polyester seams by decades even in horse harness.
https://m.youtube.com/watch?v=dw43Isosh_s
If you can't run linen through a machine the machine isn't set correctly or there's something wrong with the machine it just requires a little know how and effort, also wetting linen makes it stronger.