Good evening John,
We answer this question regularly. A surveyor would usually show this as a problem on there report as this does cause the following; debris in the loft, pests and plenty of through draft. Although not integral to having a waterproof roof the felt certainly is beneficial to have in good condition, if any water was to ever ingress this does provide a secondary barrier too.
In order to replace the felt correctly the batten and tiles would required to be removed and replaced.
I hope that helps.
Essex roofing limited.