Decay of supercurrents connected to non-superconducting zones?

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TL;DR Summary
Will a persistent supercurrent in a superconducting (SC) aluminum ring decay, if we connect the SC aluminum ring to an aluminum wire and the remote end of the wire is located in a separate chamber with T > Tc (or H > Hc)?
This question is more complicated than it seems, most physicists cannot answer it unambiguously and there is no experiments to the issue. Imagine, a persistent supercurrent flows in a SC aluminum ring. Then we connect the SC aluminum ring (without solder) to an aluminum wire, the second end of the wire is in a separate chamber with T > Tc (or H > Hc) and is not SC. The temperature of the SC ring is stable below Tc. Thus the SC ring is directly connected to a non-SC zone where electron pairs dissipate their supercurrent momenta on atom lattice. Will the remote non-SC zone suppress the persistent supercurrent in the SC ring?

Experimental setup to the question is shown in Figure 1 in
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