I use a pay-as-you-go phone

My mobile handset came out of the arc, it will take (not very good) photos, send messages, tell me all sorts of things I don't need to know such as the time in Tokyo,as well as the date and time etc.
I use it for making phone calls when I'm away from home, and sending the odd text message to a friend who sends copious messages.
Its fine, it does everything I ask of it.
BUT
I got to the supermarket to pick up my 'click and collect' order. It was early and no-one was there.
A message on my phone said 'Tap here to let us know you've arrived'.
I couldn't do that because my handset isn't a touchscreen. There was no phone number to call, there was a door - firmly shut - and no-one in sight apart from a queue to enter the store.
So I had to join the queue, in the drizzel (it was raining here 'up north' at the time) and eventually made my way to the customer services. They sorted it.

My question is (finally )
If I bought a touchscreen handset (you can get them for about £30) would I have been able to TAP here' to alert them, even though my SIM card is pay-as-you-go?

I have had to shop at a different store across town because they have a bell you can ring to tell them you've arrived.