EMI Session?

Hi David - yes, according to Morrissey, they did do a demo for EMI in 1982. Here's the relevant section from my book (p68 of the hardback version).
Best wishes, Len
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Without doubt The Smiths were utterly different, completely unlike anything else in the British music industry in the early Eighties. Against all the odds, stacked against him throughout his childhood, Morrissey was emerging as a charismatic frontman, a provocative spokesman for an independent generation. The Smiths knew where they were going but had they signed to the right record label to get them there?
Interestingly Morrissey later told me that Rough Trade weren’t the only London-based label initially keen to sign The Smiths. Before signing with Geoff Travis, the band had come close to joining EMI Records.
“It’s hard to say what would have happened if, for instance, The Smiths had been on a major label initially. EMI were the first record label that were ever interested in The Smiths and actually put The Smiths in the studio in 1982 and consequently rejected the outcome.”
What tracks did you give them?
“We gave them ‘What Difference Does It Make?’, ‘Handsome Devil’ and ‘Miserable Lie’ which they deemed unsuitable. It’s quite interesting that two years later one of those songs was a Top 20 hit.”

Has the Drone demo ever made it out?

Not to common circulation yet.
Stephane