If you want to take a shortcut, the tunnel is probably ok, even if there is a lot of traffic. There is a small sidewalk on the side that you can ride on... but not very fast. So be prepared for about 20 minutes in the tunnel.
I planned poorly and drove through the tunnel. The only advantage is that the tunnel is steep. I raced through as fast as I could with my tail light flashing very brightly, but I was terrified that a truck driver playing on his cell phone would run me off the road. The extremely wide gaps in the manhole covers running in the direction of travel are also not without their problems, and a tire can easily sink into them. It is better to calculate more elevation and avoid them.