The LNER was very pro-electrification in the 30s and had been encouraged by the success of the MSJ & A 1500V DC scheme in Manchester (jointly with the LMS). It did get as far as commissioning reports for the ECML to Leeds / York , GE to Norwich and London Suburban, but it was always financially precarious and would have required substantial government assistance. There were no plans to electrify the GC Extension.
Yes, Woodhead was primarly about coal traffic, reducing working expenses and dealing with the notorious tunnels and precipitous Worsborough incline. It did have an eye to passenger operation as well, however, for the Fallowfield Loop round to Manchester Central was included in the original scheme, and indeed the station canopies en-route were cut back in anticipation. A second stage envisaged extension to Liverpoool via the CLC (jointly with the LMS). A third rather more vague phase envisaged linking up with ECML at Retford or Grantham (via Nottingham).
The post-war world was somewhat different with main-line dieselisation becoming an option, using 'twins' like the LMS.