I can reliably report that it works here.
On Monday, after the meerest nanosecond of inattention with a pair of scissors(!) I had occasion to report to a local clinic.
You will need your passport, health card, plus, clearly, the wounded part!
Very quick and efficient service. The wound was closed using some kind of superglue, magic stuff.
A notice by reception desk asked for non Spanish speakers to have a translator in attendance, but in practice, they were most obliging. Sangre is blood, by the way! Plus 'ooooyabasta' is much the same in any language when disinfectant is applied.
You can apply online to get the card, so easy even I could do it!!