Surely not? Why electrify for one train per hour west of Salisbury, serving a very rural area? This would surely be one of the lowest priority areas for electrification?
This line gets a remarkable amount of attention on this site
Indeed, if the line is to see electrification it would be sections of it. The most likely would be the section within Exeter from Sr Davids to the junction for Exmouth where there's 3tph.
Likewise, around Salisbury where you've got 2tph with the Waterloo services as well as the Salisbury 6 services (Salisbury, Romsey, Southampton, Eastleigh,, Romsey), the Salisbury Bristol services and the Cardiff Portsmouth services.
You might be able to justify from Basingstoke if you then created the ability to turn the Basingstoke Stoppers asking the line rather than them take up a lot of platform space and crossing on the flat east of the station and the capacity issues that creates.
However, as the Basingstoke Stoppers arrive just 10 minutes ahead of the services towards Salisbury (although, as this has to await the departing service it's often held for a minute east of the station so there's a little more padding than that) and leave Basingstoke for Waterloo 4 minutes ahead of the services from Salisbury it's all rather tight. Although, it could be possible to leave Basingstoke, head down the WofE line, have the service go into the London bound platform of the station it's turning at and then sit at Basingstoke for (say) 3 minutes before continuing towards Waterloo to give some timetable robustness.
If the Basingstoke Stopper was running late, then it could be turned at Basingstoke still, and whilst this would constrain paths again it would still mean that platform occupation was far less than is currently the case and would only be an issue if the service was more than 8 minutes late.
Andover (23 minutes from Basingstoke) could work, although you'd need an extra 30 minutes of rolling stock capacity to undertake the round trip (basically the units spend 30 minutes at Basingstoke, so they would be at Andover when they would have otherwise been leaving Basingstoke, so you'd need extra units to have left Andover 30 minutes earlier to cover that service).
That would give you the following timings:
Stopper
Basingstoke xx:28/xx:58
Andover (P1 arrival) xx:51/xy:21
Andover (departure) xy:00/xy:30
Basingstoke xy:24/xy:54
Salisbury services
Basingstoke xx:08/xx:38
Andover (P2) xx24/xx:59
Andover (P1) xx:36/xy:05
Basingstoke xx:55/xy:28
Which is all rather tight, but there could be a bit of a pause added at Basingstoke for the up, former Basingstoke Stoppers, service with the departure time at Andover shifted earlier a little.
With the minor stains between Andover and Basingstoke served by the former Basingstoke Stoppers (and so seeing 2tph) it could be possible to skip then on the Yeovil services at these stations.
This night not be ideal as whilst it would be a possible to change to the Yeovil service when travelling towards Salisbury with nearly no time plenty but would require a 25 minute wait at Andover when returning from Salisbury. Having said that with 2tph rather than 1tph there would be a wider number of services and so there would be a fair chance that the actual "I want to arrive/leave at xx:xx and so need to catch this specific train" wouldn't be much different than the current situation as there would be the potential for far less waiting at (say) Salisbury and Whitchurch (WCH) for the 1tph to turn up.
For example in the evening the existing service from Salisbury is at 17:47 (arriving at 18:14), if you can't get to the station until after then you'd have to wait until 18:47 to head home (arriving 19:14). However, with the above change, the 17:17 and 18:17 services become available. These would arrive at Andover at 17:37 and 18:37, allowing a change to the 18:00 and 19:00 service arriving to Whitchurch 18:09 and 19:09.
Whilst it you can work things well that's slower than the current situation it's not much different if you're running aren't ideal. Although that's only if you skip those stops in the existing services (and even if you did for most of the day you could always keep them in the peak hours - which would make commuting from/to those minor stations to/from Andover and Basingstoke have 3tph for some hours of the day - potentially useful if there was to be some significant house building to happen near those stations).
That could justify the electrification between Basingstoke and Salisbury (as previously mentioned the other services which is they had batteries would also benefit) and could allow works to the junction at Basingstoke to create extra capacity to be delayed as some of the benefits of those works had been dealt with already.
Obviously the ideal would be to extend the Basingstoke Stoppers to Salisbury, however with the number of existing trains there you might struggle to fit them in.
(I think that the reason the WofE line gets a lot of attention is that there a lot of options as to what could be done with it, and so it makes for interesting discussions, even if there's not a lot likely to change anytime soon).