Yes, an eligible receiver-by-number may play in an ineligible position, similarly to how an ineligible player-by-number may line up in an eligible position. In both cases, they must report to the referee, who will then report it over the intercom or simply directly to the defensive huddle (though, usually over the intercom), and will do so each down the player remains in the game (and the player must report each down). Rule 5-3-1 states this:
ARTICLE 1. REPORTING CHANGE OF POSITION. An offensive player wearing the number of an ineligible pass receiver
(50–79 and 90–99) is permitted to line up in the position of an eligible pass receiver (1–49 and 80–89), and an offensive player
wearing the number of an eligible pass receiver is permitted to line up in the position of an ineligible pass receiver, provided
that he immediately reports the change in his eligibility status to the Referee, who will inform the defensive team.
He must participate in such eligible or ineligible position as long as he is continuously in the game, but prior to each play he
must again report his status to the Referee, who will inform the defensive team. The game clock shall not be stopped, and the
ball shall not be put in play until the Referee takes his normal position.
The New England Patriots played with this extensively during the AFC Championships last year (2014-15). As such, a rule change was made for the 2015 NFL championship season by way of a note on the preceding rule (5-3-1):
Note: An offensive player wearing the number of an eligible pass receiver who reports as ineligible must line up within the
normal five-player core formed by ineligible players. The player cannot be more than two players removed from the middle
player of a seven-player line.
This is because the Patriots would have lines where, for example, two players with eligible numbers were located on the line, one of which where the "tackle" normally is (2 players left of the center), and one in the normal "tight end" position (3 players right of center), but the "tight end" is ineligible and the "tackle" is eligible. That was legal at the time, but no longer is.