No, don't go at night. Don't go unless you are part of an organized tour. Drawbridge is along the train tracks used by Amtrak and ACE trains. At night, freight trains also use the tracks, and not on a set schedule. If you are at the wrong spot and a train is coming, there is literally nowhere to go except for a swim in the mud. I went there on a tour, I think through Palo Alto Baylands. I'm not sure if tours are offered anymore, a quick google search didn't come up with anything. It's an interesting spot, especially if there is someone along who knows the history, but there really isn't that much to see anymore, most of the houses have sunk into the mud.
IMHO the biggest risk out there is getting caught not the trains. The tracks leading up to that area have clear sight lines for miles. I've been out there 4 or 5 days over the years and have only really had to deal with trains a few times, and you always knew they were coming with many minutes to spare (10+ for a slow moving freighter, to just under 5 probably for an ACE train). Not to say it isn't dangerous, but if you can jump to the left or to the right and are worried about some mud I'm not sure that this is the place for you to explore :)
On the other hand I've had several friends get nasty fines from LEO's while out there, or on there way out there. YMMV
