It could lead to a south Warwickshire to north Warwickshire service which could do Leamington-Coventry-the Ricoh-Bedworth-Nuneaton, as I am sure there is a sprinter shuttle service between Coventry and Nuneaton so that could extend to Leamington aswell.
The sprinter shuttle (generally a Cl153) operates hourly through the day, with an intreaging 1h45 gap mid morning. It is the remains of the former Leicester - Coventry service, which ceased when the new platforms were opened at Nuneaton, meaning it was no longer possible to operate.
There was an idea a few years back for through diesel services to run Leicester - Nuneaton - Coventry - Leamington - Banbury - Oxford.
Table 57 of the NRT was even adapted to show the last three stations in preparation, but it never happened.
Clearly all of the proposals for the Leamington to Coventry line will have to come together. Therefore I would expect doubling to come first, then the wires and Kenilworth soon after. As others have said it is unlikely that XC would stop the Voyagers at Kenilworth (although they could be forced to). If they don't then it would need to be served by an additional service from somewhere.
With the wires through to Nuneaton as well then one could envisage a joined up NUN-COV-LMS service, however with a current through journey time of thirty two minutes (electrification would speed this up by a few minutes, but the stop at Kenilworth and pathing allowance at Coventry would consume this), an hourly service would be impossible without needing a second set.
Most likely would be a(nother) recast of the BHM-COV route, which I believe could potentially result in:
*Four paths VT to London
*Two paths XC to Reading & beyond
*Two paths LM to Northampton & London
*Two paths LM stoppers to Coventry, one of which runs on to LMS.
and hopefully some freight paths as well.
This would clearly need to make use of the passing ability at International, and therefore slow up the stoppers, however cross platform interchange between slows and fasts would be available so in some cases offer a quicker journey for users of the local stations.