but don’t these students just do a CPL LST and these ratings are issued at the same time of licence issued.
CPL is a licence not a rating and to teach for a CPL you require 200 hours instructional experience as a FI. There is no such thing as a frozen ATPL.
To teach at an Integrated school you need a CPL as the candidates are training for a CPL. You can train for the PPL elements only at an Integrated school with less than 200 hours.
Don't forget that to complete the IRI Course and teach for the IR you must also hold an IR
Accruing IFR time can be a problem, remember it is IFR time not IMC. To claim IFR you would have to have been qualified i.e. have held a valid IR or IMC rating and pre EASA all night time was IFR.