Would you be able to feel a labral tear in the hip when it first occurs?

Not necessarily: Labral tears can be degenerative and happen over time or acute. However, even the acute ones you would just have groin pain but not be able to be specific and call it a labral tear.

Possibly: Some people will report a tearing feeling or the sudden onset of anterior groin pain, some will report that they began to notice their hip "clicking" after an injury; all of which can potentially be associated with a label tear.