Yes, you can just go in and buy from them, but there are some items which they won't sell to non-hairdressers/other beauty professionals - scissors, some bleaches/dyes and other chemical-y things.
I haven't been in to my local store for a few months, but if things are still the same as they used to be, they'll add VAT onto the prices at the checkout so keep that in mind when you're stocking up!