Does a type rating give a person the privileges of an instrument rating in any category or class of aircraft which he/she is certificated in?
61.63(d)(1) requires that if you don't have an ATP that you hold an instrument rating to obtain a type rating. The type rating itself does not grant instrument privileges.

(d) Additional aircraft type rating. Except as provided under paragraph (d)(6) of this section, a person who applies for an aircraft type rating or an aircraft type rating to be completed concurrently with an aircraft category or class rating—
(1) Must hold or concurrently obtain an appropriate instrument rating, except as provided in paragraph (e) of this section.

Paragraph (e) exempts aircraft incapable of instrument maneuvers and instrument flight from this requirement.
This does mean that you can do the instrument checkride concurrent with the type rating. If your hypothetical PP-ASEL gets typed in a citation, he will end up with a PP-ASEL with instrument airplane rating and the citation type.