I'm not entirely sold they go pitching regardless. These are BOS drafts under theo rounds 1-10
2003
49 - Alvarez, Abe
84 - Vaughan, Beau
114 - Papelbon, Jonathan
144 - Marshall, Brian
174 - Corn, Jessie
264 - Wilson, Jonathan
2004
94 - Dobies, Andrew
125 - Hottovy, Tommy
155 - Schroyer, Ryan
185 - Meredith, Cla
245 - Bono, Kyle
2005
26 - Hansen, Craig(wasn't their first pick as they took Ellsbury 23)
42 - Buchholz, Clay
47 - Bowden, Michael
138 - Blue, Scott
258 - Zink, J.T.
318 - Guyette, Kevin
2006
28 - Bard, Daniel(again they took Place, Jason 27th)
40 - Johnson, Kris
44 - Clay, Caleb
71 - Masterson, Justin
103 - Cox, Bryce
163 - Richardson, Dustin
313 - Snyder, Kyle
2007
55 - Hagadone, Nick
114 - Huntzinger, Brock
144 - Province, Chris
264 - Mills, Adam
2008
45 - Price, Bryan
85 - Fife, Stephen
108 - Weiland, Kyle
262 - Lee, Michael
322 - Ruiz, Pete
2009
77 - Wilson, Alex
198 - Kline, Branden
228 - Younginer, Madison
288 - Volz, Kendal
2010
39 - Ranaudo, Anthony
57 - Workman, Brandon
233 - Hernandez, Chris
263 - Price, Matt
293 - Barnette, Tyler
323 - Dahlstrand, Jacob
2011(Theo's last draft in boston)
19 - Barnes, Matt
36 - Owens, Henry
142 - Ramirez, Noe
202 - Pena, Miguel
232 - Kukuk, Cody
As an aside I'd like to talk about the work he did in 2011. Barnes from my understanding is still someone decently regarded. Their second pick was Swihart(26th), their third pick was Owens, their 4th pick was Bradley Jr., and they got Mookie Betts in the 5th..... jesus. Regardless, Barnes was the only time they used their first pick on pitching unless you count 2010 when they didn't have a 1st round pick. I only listed rounds 1-10 and while there's a lot of "WHO!?" there you also have guys like Masterson and Buchholz who've been solid starters. Papelbon, Meredith, Bowden, Bard, Ranaudo, and Workman have all mad the majors with varying degrees of success primary as relievers.
This is perhaps a bit slanted as BOS didn't pick top 10 during that reign. I'd could honestly see them doing another similar move to go over slot on some arms later in the draft by going under slot on a positional player.