I think I have two thongs to say here.
Yes, NVQ L4 does confer the necessary H&S competence to implement and run an SMS in a Nursing Home. But, competence doesn't just rest on H&S qualifications (it's that old chestnut again). The first part of the definition of competence in the management regs is 'an understanding of relevant current best practice', and that's where simply having NVQ 4 (or a BSc or L6 Dip, for the sake of this argument it makes no difference) doesn't prove competence in a Nursing Home setting.
What are you going to have to deal with in a Nursing Home? Here's a sample; skin integrity, infection control, management of medicines, bed-rails, management of medical gases, choking, challenging behaviour, confusion, manual handling, COSHH... Maybe those latter sound familiar to most of the people reading this forum, not too sure about the others. OK, medicines will only impact on H&S in a peripheral sort of way, but the other things will be either wholly or partly in the H&S camp.
H&S, in short, isn't H&S, and a H&S qualification will give the holder some technical knowledge about the way H&S can be managed, and why it should be, but it won't necessarily convey the detailed understanding of an alien work environment. If you acquire your NVQ L4 while working in a care environment it probably will confer competency, if not it will leave gaps in understanding which will need rapid filling.
We have 6 Nursing Homes, most people think of old people when they think of nursing homes; well, that's wrong, old people, if they are in a home, are usually in a care home, because they need care. People in nursing homes need nursing, in our case that's because they have any one of a whole series of complex conditions, and the H&S implications are ramified and complex in their turn.
So in short, probably no, would be my answer; not because it's NVQ4, but because whatever H&S qualification you have, you also need some kind of experience in a healthcare environment. It's possible to start as a H&S person in a nursing home without previous healthcare experience, but you won't be competent, and you'll have to be a fast learner,
John