So, as I understand it you are playing 4th Ed? I would have a good long conversation with this player before he ultimately makes his character. Something to the tune of "You can do this, but being a subspecies that is almost universally reviled in polite society is going to be challenging at best. Also, it presents a LOT of technical obstacles in just how to live day to day, on top of being a Shadowrunner".
Basically instead of simply blanket saying "NO" to all player requests in any game I run, I try and think of if it's reasonably possible to do what the player is asking, and a lot of times it isn't. In this case, it would be possible for A player(not necessarily the power-gamer you described) to do this, but beyond mechanics let's look at what it would require.
1) They have to maintain a low-attention lifestyle, as almost all Runners do. Additionally, their lifestyle would have to be modified based on their living requirements considerably(No UV light, likely out of sight of most normal metahumans, etc).
2) They have to secure a clandestine way of acquiring food regularly, food obviously being people. Now, if they're smart, they could set up and scout ahead for homeless, SINless people, vagrant communities, etc, definitely doable, but just takes time and preparation.
If he establishes the above in some decent manner, then comes the issues with being a Vampire and Shadowrunning.
1) As with the aforementioned distrust of Vampires, he will need to find a way of contacting Mr Johnsons who are willing to work with him. Granted, with a team this is easier, as another person can secure the job and leave him out of that aspect. However, if a Johnson who has a hate-on for the undead finds out he's on the team, there could be fallout afterwards, betrayal, etc.
2) All Runners try to actively avoid getting spotted on a job, data trails, getting their face on a camera, etc, however a Vampire would have this multiplied. He not only has to worry about being identified as a member of the SINless community of Runners for hire, but as a very real and present threat within said community. Yes, sometimes certain Vampires and Ghouls and such are more accepted by other denizens of the shadows, but not always. Getting made on a job for him would be magnitudes worse than for another member of the team, in all likelihood.
3) Let's assume for a moment the team gets screwed by a Johnson, or a run goes wrong, or somehow they get Lone Star/Knight Errant/etc after them. For regular Runners, this may constitute a detective investigating and asking questions, or a private eye watching them for someone, or maybe even S.W.A.T. kicking in their door if shit gets really real. Now, add an anonymous tip in that one of the suspects is a Vampire. Immediately you likely have a High Threat Response team, backup ready at the drop of a hat, etc. Basically, threats like that are taken seriously. So for him, when it rains, it pours.
Sorry to rant, but these are all reasonable considerations your player SHOULD have. If he is ready to deal with them, and is willing to play smart and make preparations and plan ahead, it can absolutely work, and he might have the time of his gaming life. Might also go horribly, horribly wrong for him in a very short amount of time.
