No, says the EAT, on the facts in in Bangura v Southern Cross Healthcare.
The employee worked in a care home owned by Southern Cross Healthcare Group plc. She was summarily dismissed on ground of misconduct about six weeks before the care home was transferred to Four Seasons Healthcare. At the time of transfer she had an appeal pending against her dismissal, but it had not by then (or at any time since then) been determined by Southern Cross.
An employment tribunal held that the TUPE Regulations did not transfer liability to Four Seasons since the employee was not employed by the transferor immediately before the transfer, as is required by Regulation 4(3) of TUPE.
She appealed on the ground that this seemed inconsistent with the earlier decision of the EAT in G4S Justice Services (UK) Limited v Anstey  IRLR 588. In that case an employee in a similar situation, whose appeal against dismissal was successful, transferred to the transferee under TUPE on the basis that the original dismissal, by virtue of the successful appeal, had been overturned.
However, in Bangura, the EAT distinguished G4S. In G4S the appeal had been successful and the dismissal negatived. In the absence of a successful appeal, the normal principle applies, namely that a summary dismissal takes effect immediately and terminates the employment at that time. As the dismissal had nothing to do with the transfer, the employee was therefore not employed or deemed to be employed in the undertaking immediately before its transfer.