Is it correct to say 'Do you know him in person?'

This is tricky. All the dictionaries I've checked in license the action verb / punctive usage, and Macmillan could actually be considered to restrict the phrase by adding a punctive verb:

do something in person ...

to do something by going to a place or person rather than by writing, telephoning, or sending someone else

You have to collect your tickets in person.

I’ve talked to him on the telephone and in person.

The CDO entry is not quite as prescriptive:

in person

by meeting with someone rather than talking on the phone, e-mailing, or writing to the person:

You must apply for the license in person.

though I'd say we can assume the 'to do something' here too.

AHD muddies the waters by adding the synonym 'personally':

in person

In one's physical presence; personally:

applied for the job in person.

and of course 'personally' doesn't require a punctive verb: I know her personally. (stative) I'd consider this entry misleading.

Collins seems to give a tighter if not totally decisive definition, but adds a second sense (which, however, seems to require an action verb if not a punctive usage):

in person

a. actually present

the author will be there in person

b. without the help or intervention of others

And ODO again seems inconclusive (but note that all examples given have been with action verbs):

in person

With the personal presence or action of the individual specified.

he had to pick up his welfare cheque in person

Google searches show that expressions like 'know him in person' are far from rare, but these Google Ngrams show that 'know him personally' etc are by far the more popular variants. They'd be my choice.