Adamant1
It appears that it does. Although it goes slightly north along Park Avenue and then snakes around the veterans memorial. I mapped it until West San Carlos Street, where it goes under the road and connects with the other trail, but my eyes tarded out at that point so I stopped. Here's a map from the cities website that has it if anyone wants to take a look and map the rest https://sanjoseca.gov/DocumentCenter/View/9462