Yes, "stand for [someone]" can be used to mean "represent" or "be here in his place", but it is not a common construct, and is usually only used in situations where the representation is formal and legal.
E.g., a lawyer stands for a client, or a colleague may stand for a member of a board of directors during an important vote that the latter cannot attend in person.
In most other cases, a more natural/modern phrasing would be "stand in for" or "substitute for": "Elberich was sick, so I had to stand in for him at the presentation without any practice".
"Stand for" may also be used (but again, only rarely) in the sense of "support" or "stand beside", for example the witnesses at a wedding are said to "stand for" either the bride or groom.
In the specific case you're suggesting:
'I know Christian would want to be here, but I stand here for him.'
I would say that sounds perfectly natural, but maybe not in the sense you intend. I read that as "I stand here, for him". In other words, the "for him" is an adverbial phrase giving the reason why you are standing here, not part of a phrasal verb. In contrast,
'I know Christian would want to be here, but I stand for him here.'
would force the "stand for" interpretation (that you will be representing Christian / voting on his behalf within this event / meeting), but it sounds much more formal or stiff.
If the sense of representation is important to you, some other more common ways to express "I'm here in his place" are
- I'm here on his behalf
- I am representing him here
- I am standing in for him
- I am substituting for him
Note that the first two imply that you are acting under Christian's direction, while the latter to merely suggest that you're replacing him.