No. To be eligible for statutory sick pay (SSP) an employee must have performed some work for the employer under their employment contract (sch.11 to the Social Security Contributions and Benefits Act 1992).
So, although SSP is a day-one right, this does not apply to the employee's first day of work.
An employee will be eligible for SSP on their first day if they had previously worked for the employer under a different contract and there is a gap of no more than eight weeks before the start of the new contract.