Yes, that is the way to do it.
This arrangement is well known to all court users (prosecutors, magistrates and their legal advisors). It is almost always successful. Since this site has been running there have been no reports of refusals and this site's predecessor (Pepipoo) had knowledge of only one (both, as far as I am aware).
I think the police and their prosecutors recognise that very often the "FtP" charge comes about due to administrative difficulties (lost or delayed post, unnotified change of address, drivers' misunderstanding of their responsibilities, etc). They also understand that the consequences of conviction for that offence are usually far more profound than for speeding.
So long as they are happy that no advantage is being sought (say, if the actual driver was trying to avoid a "totting up" disqualification) they are content to accept a guilty plea to the underlying offence and will drop the FtP charge (which, if continued, might often involve them in a trial).
The "leverage" that the driver has is that without guilty plea, a conviction for speeding cannot succeed (the police have no evidence to prove who was driving). An offer to plead guilty secures that conviction with little or no effort and in exchange all the police must do is drop the other charge. he willingness of prosecutors to undertake this agreement is illustrated by the fact that, in circumstances like your wife faces, they almost always raise both charges (speeding and FtP) even though they do not know who was driving and the speeding charge cannot possibly succeed without a guilty plea.