Resoldering the old relay effectively renews the connections that may have come loose over the years due to vibration/heat. Once the connection is repaired the relay will operate like it did before the cracks formed. - To answer your question, assuming the internal electronics are ok, then your resoldered relay should work like new and allow you to avoid the costly relay replacement altogether.

Therefore, don't toss the old relay, instead resolder it and leave it in your car as a spare for replacement when you stall on the road the next time (hopefully a long time from now i.e. 7-10 years with the new relay in place).

Cheers,

Tim