Are bikes allowed on the Metro at all times? They aren't in DC. And no, locking up a bike for hours on end is not necessarily safe. Be sure and get a POS for that, with no extraneous stuff (lights, etc) that can be stolen. Lose the quick release skewers on the wheels or get locking skewers. Lose the quick release seat latch. use multiple locks of multiples styles (u-lock and chain lock) when locking up the bike. Park next to nice bikes
A folder, if small/light enough that you can indeed take it into where you go, solves the lockup issue/worry. Your call on that.
I commute on my folder (via mass transit). I also wheel it straight into the supermarket and use its baskets as my shopping cart. All good reasons to own a folder.