The likelihood of this happening depends on how much was dismantled when they changed the head gasket.
This product is designed to remove deposits from engines with hydraulic tappets. It sounds to me like the garage have botched the job and are trying to mask their mistakes. I wouldn't expect this product to give any meaningful benefit on a 500, which hasn't even got hydraulic tappets.
Older 500's can be a bit tappety when stating from cold, but if you've still got tappet noise when the engine is warm, all is not as it should be.
Right now, the first thing that needs to be done is to remove the rocker cover and check the valve clearances. If they're out of limits, this is rectified by changing shims; not particularly difficult, but you need the right tool to remove them, a micrometer to measure them and access to suitable replacement shims.
If the valve clearances have been disturbed during their repair, and they haven't reshimmed where necessary, my main concern would be that one or more of the clearances is now too small. This is much worse than being too large (which is what causes that tappety sound); if this has happened, the likelihood is that you'll end up burning the valves and most likely ruining the cylinder head completely.
If you have the skills and facilities to remove the rocker cover and check the clearances yourself, then do it now (you'll need a new cover gasket); otherwise, take it to a garage that knows what they are doing, and ask them to do this. If the clearances are way out, I'd be seeking some form of reimbursement from the garage that did the original repair.
Given your location,
Small Car Services is one garage I'd recommend for performing this check, and carrying out any rectification which may be necessary.
You're not going to fix this for any length of time by pouring some sort of magic potion into the engine.
