Yes, several times. I see no reason why not. Menstruation is a fact of life and the products needed to deal with it are no more embarrassing to buy than any other kind of toiletry. I wouldn't hesitate to ask him to buy shampoo or shower gel, so why would I worry about panty liners and tampons?
I had to get my partner to get maternity pads for me once. he took our toddler who insisted on carrying them and walking around the shop talking about "mummy nappies" lol. I'm pretty sure that I've had to get him to buy tampons before - I wrote out EXACTLY what I needed on the shopping list, including the colour of the packet and his venture was successful!
No. I always knew he was a little embarrassed about it and since I was embarrassed about it, and it was my problem, I always shopped for myself. It is a fact of life but so is the occasional requirement for a jock strap - and I wouldn't go shopping for one of those for him.