Not a VGA Connector
That 15 pin connector is not a VGA connector, even though it is the same style of connector as VGA uses. It is a digital out port for the LCD panel data. If you want to use the output from that port to display video you need circuitry which will convert the digital screen display into a format that your target display will understand.
If you connect a VGA monitor to that port you will almost certainly destroy some internal components of the Portable.
The mystery component is indeed a power management circuit. It came in at least two different styles.
If would be interesting to see you give the Outbound Laptop Model 125 the same treatment. It came out in 1989 or 1990 (can't remember which) weighs 9 or 10 lbs and has similar specs to the Mac Portable -- oh, and runs the Mac OS, almost forgot that tidbit.
The main differences are that the Model 125 weighs 2/3s as much, uses a standard lead acid camcorder battery which is *still* available new, has SIMM sockets for expansion (only 4 MB max. though, not 8 MB), uses an internal 2.5" IDE hard drive (long before Apple used IDE), has a detachable keyboard with pointing device (IR interface), and has four internal SIMM sockets dedicated to a RAM Disk with a capacity up to 16 MB. With one's OS and applications on the RAM disk, the hard drive could be left spun down except when saving documents. And it booted the OS and launched apps incredibly fast.
The disadvantages of the Model 125 were that the internal hard drive displaces the internal floppy drive -- you could not have both. SCSI connectivity required an external adapter. The SCSI adapter or the external floppy could be connected but not both at the same time. The display was passive instead of active, and the battery life was shorter.
One notable advantage of the Model 125 was that with the SCSI adapter connected, one could put the Model 125 into Target Mode and the hard drive and Silicon Disk (RAM Disk) (if any) were available to a host computer connected via SCSI. This was a feature that Apple would not have until the first PowerBooks came out. I've been told that they actually bought this technology from Outbound.