Note: This answer is posted after the OP has obtained first hand experience, simply for the sake of noting down what I have found in my brief research.
Short version: Yes, despite the TfL journey planner and route list saying 105 does not go into Heathrow for outbound (from Greenford, to Heathrow) trips, Bus 105 does go into Heathrow Central Bus station according to multiple sources, including some from TfL themselves.
Document from TfL says yes
A 2011 public consultation from TfL on route 105 included a map that clearly shows that outbound bus (from Greenford) goes all the way into Heathrow Central Bus station:
While the consultation result is not available on the page, given the route no longer serves The Compass Centre (see the route of 105), the change is clearly introduced. There are no further consultation on route 105 as of the moment this answer is typed, and hence it is not possible for them to permanently alter the route between then (and in the near future).
Data from TfL says yes
Someone has submitted a Freedom of Information (FoI) request to TfL, asking for the times that 105 buses has departed each stop in first half of 2018.
The response from TfL contained a spreadsheet, in Direction 1 (from Greenford to Heathrow), Heathrow Central Bus Station is on the last column, with the times recorded usually a few minutes after the previous stop Nene Road (purportedly the terminal).
Communications from TfL says yes
A quick search on Twitter suggests Heathrow-bound 105 buses do go into Heathrow. As the TfL Bus account do apologise if buses cannot get pass the tunnel into Heathrow (emphasis mine):
Route 105 111 140 285 U3 X26 returned to line of route following East Ramp Heathrow protest (Nov 2016)
Heathrow Tunnel - Routes A10, U3, X26, 285, 105, 111, 140 are terminating early & unable to serve Heathrow due to a car stuck in the tunnel (Nov 2015)
Bus fans says yes
Multiple videos and photos uploaded recently shows that the buses themselves are advertised to go to Heathrow Central.
Example video from BusesInLondon (June 2018): Link
Example photo from Adan Matthews (circa 2018/2019 by registration plate of the bus): Link
Example photo from hassaanhc (Mar 2019): Link