That's precisely what I do, as my habit of buying only secondhand bikes or salvaging dumped ones means I have a pile of old secondhand tyres.Many people use old bikes with old cracked tyres esp as short range pub/shopper bikes. If you are going further or to work, you need tyres you can rely on.
For local use within a range of 2-3 miles from home I will ride on any tyre that will hold air, no matter how scruffy. The worst case scenario is an annoying walk home.
On the bikes I do my longer rides on, I'm pretty fussy about tyres though. I use the excellent Schwalbe Marathon Greenguards or Delta Cruiser+, depending what is available on a good deal.