I doubt it. Once you isolate the routes it's just plain vanilla double track OHLE, abet adjacent to a double track 4th rail installation, no different to what is the case along the London section of the WCML (and what will be the case from Finchley Road to at least Neasden Junction once Chiltern gets its wires). Given the modern propensity against portals, you could probably even keep all the uprights on the down side, well away from the 4th rail lines.
Based on current experience, vanilla double track OHLE will cost something like £9m per route kilometre. It will get very expensive very quickly.
I doubt truncating the Metropolitan Line to Rickmansworth and dumping people into Marylebone (a markedly inferior terminus to Baker Street is almost all ways, let alone through trains to Aldgate) will be particularly popular with the user base either.
Chorleywood, for example, has far more traffic on LU than it does on the Chiltern.
If the Metropolitan line were extended to Aylesbury or AVP that certainly would be an operational headache for Chiltern at Aylesbury as various walking routes cross the line and at least one platform would be shared between the Met operation and Chiltern. Anyway this is all pie-in-the-sky as there is pretty much zero chance of the 3rd/4th rail being extended north of Amersham.
If the Metropolitan Line extends to AVP then Chiltern operation would be restricted to a single platform at Aylesbury for the rump service via Princes Risborough.
There would be little need for it to to share platforms.
I'd say, even if it is unlikely, there is considerably more chance of the Met extending to Aylesbury than the Chiltern Main line receiving the well over billion pounds it would take to electrify.
Or the couple hundred million pounds required for reelectrification to Aylesbury via Amersham.
? The 350/1 are dual voltage as are the 387s which both used it daily hassle free and currently the 700s use it day in day out with no issues at all.
It will require a fleet of dual voltage rolling stock to be provided which would otherwise not be required.
This will require additional maintenance work that would not be required otherwise, and place restrictions on diagramming that would not exist otherwise.
In addition, it would require electrical work on the LU to convert the line from four rail to de-facto third rail operation.