If the tensioner had completely disintegrated then yes (or no oil pressure). If it only happens when warmed up then it's more likely an weak tensioner and/or stretched chain, as the tensioner is tensioned by both the engine's oil pressure and a spring inside it. Both are needed to keep it in tension, if one of the two is missing (your case
probably the spring inside the tensioner) and in
@stickemupp92 's case
probably the oil pressure (he has a much more serious issue on his hands than you).
As the engine warms up the oil pressure slowly falls to operating pressures. This reduces tension on the chain tensioner. If one of the two previously mentioned requirements in insufficient or missing, getting up to temperature will reveal the 'warm rattle' MK5 GTIs are known for getting.
Of course for diagnosing is would be best to use VCDS to make sure it is actually the issue, as there's no other easy way of checking.