Its correctness, as with any language usage, will depend on your audience. In England, in most formal writing, using "he" in this context would communicate that you were either unaware of contemporary good usage, or deliberately flouting it.
[Edit, prompted by the OP:] For example, from the Transport for London editorial style guide (a major municipal highways authority & public transport operator with a multi-billion pound (dollar/euro) turnover:
Avoid giving offence by using outdated
or patronising terms and include
references to gender only when it is
essential. Using the plural can be
helpful: customers; local people;
[Edit 2] Similarly, from the Training and Development Agency for Schools style guide:
Use they in preference to he/she: if
the candidate passes the test, they
should... If possible, try to avoid
using gender specific pronouns, e.g.
candidates who pass the test should…
(emphasis in the original)