No, they wouldn't. Free tuition would revert to the old system of capped numbers and would hugely reduce the number of places available. EU students (apart from Ireland) would apply as EU citizens but would not gain free tuition. They would likely face the full cost tuition in the same way that international students do, but without the visa restriction. They would also be excluded from the capped numbers- which is why when you walk around Oxford, Cambridge or UCL you will hear a million and one American accents- its far easier for them to get into the best institutions than it is for a home student.
Yet billions in taxpayers’ money goes to supporting these institutions in the form of research funding (research-intensive university is politician speak for the universities that they went to).
Obviously we still allow home students to go to the crap universities