I don't see how we have room for him.
I think the key is what we do at the running back spot. If Olawale is going to be considered both a fullback and tailback, then we'll go with one less in the backfield (Elliott, rookie/FA, Olawale), which means we're more likely to carry four tight ends again. Even when we've gone with three tailbacks and a fullback in the past, we've shown that we always could carry four tight ends. However, to do that we usually have to carry eight linemen or five receivers.
I've got us at six receivers (Cooper, Gallup, Cobb, Austin, Hurns, Wilson/Brown/Smith), and we could even go with seven there.
Then I've got us with nine offensive linemen (Smith, Williams, Frederick, Martin, Collins, Fleming, Sua'Filo, Looney, Ehinger).
Unless we went with seven receivers or three tailbacks and a fullback, we could keep a fourth tight end and still total 25 players on offense, or we could do it even with a seventh receiver/four RBs if we only carried two QBs. For now, though, I've got:
3 RBs (Elliott, Jackson/rookie/FA, Olawale)
3 QBs (Prescott, Rush, White)
4 TEs (Witten, Jarwin, Schultz, Gathers)
However, whether we keep 25 offensive players will depend on if we want to go heavy on defense.
Right now I've got at 25 on that side of the ball.
9 DL (Lawrence, Quinn, Crawford, Woods, Charlton, Collins, Covington, Armstrong, Hyder)
6 LBs (Smith, LVE, Lee, Thomas, Covington, March-Lillard)
10 DBs (Jones, Awuzie, Woods, Iloka, Brown, Lewis, Heath, Frazier, Goodwin, Thompson)
We could even keep Daniel Ross, or stay at 25 even if Gregory is given a reprieve, by cutting one of the two extra DBs or March-Lillard ... who may end up losing their spots anyway based on who we draft. I think we'll try to upgrade TE, S, DL and RB for sure in the draft so the spots for Gathers, Jackson, and Thompson are in jeopary, while the extra DL would probably force us to go with 10 and cut either Goodwin or March-Lillard (or again, go to two QBs or even cut Ehinger off the offensive line group).
With the three special teams spots, that should cover it.