Does Dell PowerEdge T105 support EVGA Geforce 6200 256MB DDR2 NVidia PCI E Graphics Card (256-P1-N399-LX)?

No, Dell has not validated any video cards for their servers (except the latest generation).  Not "validated" or "supported" doesn't mean it won't work ... you may find one that works, but it is normally a very hit/miss game of trial/error to find one that works.

theflash is correct, add-on video cards are not validated nor supported on anything but the latest generation of Power Edge servers.

However, there are a few general things to consider if you want to try and get add on graphics working.

1. you do not have a x16 PCIe slot available but you could use the x8 PCIe slot and modify a PCIe graphics card to fit (or use x1 PCIe or PCI card)
2. a PCIe slot can feed a max of 25W to the inserted card so you can not use a powerful graphics card without some potential problems.
3. the power supply itself is also limited at about 300W and does not provide a PEG connector for a graphics card further compounding the power issues.
4. and your biggest issue is that your BIOS does not allow you to disable the onboard video adapter.

This last point will cause you the most problems as you may find it difficult to locate a card that will not conflict with and take over from the onboard video adapter. Hence the trial and error that theflash mentioned.

Should you want to hack your system to get better video, you will need to do much homework and will need to delve into BIOS modification to be able to disable the onboard video and thus avoid the trial & error of finding a card that may work.

If time or skill might be lacking, it would be much more efficient to just build a new rig using a consumer mobo and the latest i7 CPU. Building a new rig will give you much much better video and a more powerful system. You may also be able to reuse some of your old components in the build saving some money. Doing this would also be much quicker than building up the skills to: hack the BIOS, mod the PCIe card, mod the MOBO to feed 75W to the card AND find another more powerful PSU that fits the Dell mobo and then mod it to feed the graphics card; unless you already have these skills and want a 'project'. Using a PCI slot with a PCI graphics crad like the GF6200 on the T105 does not make it any easier in reality but this is an old and slow card even by x1 PCIe standards.

If you interested in what may be involves, look here and here which will give you a glimps of the issues. There are more such posts within the server forum, just seach 'video'. Unfortunately it's not plug and play as likely you have already found out.