I feel 99.9% sure that Saint Arnolds will not. I have yet to just stop by a brewery and yeast was a normal commodity. I am sure that if you showed up on the right day and the right time you could at some places but I wouldn't think it is "common" or at least from my experience. A lot that I have been to rarely throw out the yeast, except for the bit that blows out before and after transfer.
Now don't let this tone down the excitement of visiting the brewery. I loved it! I am wearing an Elissa IPA T Shirt I bought from there as I type. Keep the free glass and buy another larger one so you can get a "better" sample. Also be sure to get a coozy for your pint glass. I don't know how I lived before it. The brewery is super clean and just amazing to visit. I snuck off and spoke to the brewers alone and they showed me the panel that controls everything and made the nerd in my super jealous.
I was impressed when I noticed one of their brewers making a "test batch" on a saabco if I remember correctly. It had raisins in it...... Hmmmmm. Nonetheless it was a great place to visit and I am sure you will enjoy it.