Yes they do, but, as far as I can tell, on Mondays to Saturdays only.
The 185s seem to be diagrammed for 0611*, 1153, 1448* Barrow - Manchester Airport
0841*, 1141, 1742* Manchester Airport - Barrow
The above times are Mondays to Fridays, but they may apply to Saturdays as well.
* = These journeys, at least, should be double units between Preston and Manchester Airport. Not sure about the others.
185s should also do a few Manchester Airport to Preston shorts, but there are no scheduled 185 journeys to/from Blackpool.
Only one unit is diagrammed to stable with Northern overnight (at Barrow). The other unit returns to TPE. The Barrow-based unit presumably stands idle on a Sunday.
From the Working Timetable, it appears that the
planned diagrams from May 2018 are as follows (platform numbers not necessarily reliable):
Diagram A:
(1B59 0325 SHeFfield to Manchester International Airport P3B, 0510)
Handover TPE > Northern
1N51* 0542 MIA, P3B - PREston P3, 0652
5U54* 0654 PRE P3, 0652 - PRE P6, 0719, ECS
1Y54 0728 PRE P6 - MIA P
4A, 0833, front portion
1C51 0841 MIA P
2A - PRE P1, 0949, rear portion
5U57* 1000 PRE P1 - PRE P6, 1021, ECS
1Y57* 1024 PRE P6 - MIA P2A, 1133
1C52 1141 MIA P2A - Barrow-In-Furness P
1, 1414
1Y63 1448 BIF P
2 - MIA P2A, 1733, rear portion from PRE
1C54 1742 MIA P2A - BIF P1, 2014 front portion to PRE
5N63* 2020 BIF P1 - Barrow Carriage Sidings [XBF] 2023, ECS
(This unit then works Diagram B the following day)
Diagram B:
5U91* 0600 XBF - BIF P2, 0603
1Y54 0611 BIF P2 - MIA P
4A, 0833, rear portion from PRE
1C51 0841 MIA P
2A - BIF P1, 1114, front portion to PRE
1Y60 1153 BIF P1 - MIA P2B, 1433
1N60* 1440 MIA P2B - PRE P1, 1550
5U63* 1552 PRE P1 - PRE P6, 1601, ECS
1Y63 1624 PRE P6 - MIA P2A, 1733, front portion
1C54 1742 MIA P2A - PRE P1, 1850, rear portion
5U66* 1901 PRE P1 - PRE P2, 1912, ECS
1Y66* 1923 PRE P2 - MIA P2A, 2031
1N66* 2039 MIA P2A - PRE P1, 2152
5U69* 2154 PRE P1 - PRE P4, 2216, ECS
1Y69* 2222 PRE P4 - MIA P1A, 2333
Handback Northern > TPE
(5W77 0101 MIA P1A - Ardwick Traction Maintenance Depot [XRK], 0123, ECS, rear portion)
* Service pathed for 75mph Sprinter
On the first three weekdays of the timetable, 21 - 23 May, Northern did not receive the Diagram A unit from TPE, so was left with a single 185. There were cancellations and short workings, with a 158 or Sprinter substituted on some of the other services - see discussion in Northern Timetable thread. On the first two days the same 185 seems to have ended up back stabled in Barrow overnight - it remains to be seen what will happen today (23rd).
Please point out errors in the above.