Almost certainly more than sufficient in terms of focal length, but a point-and-shoot may not be sufficient in its ability to collect enough light and render the background out of focus.
Something a bit over 100mm (35mm equivalent) is good for taking pictures of people standing 10 - 15 feet away. If you want just the face in the image, perhaps around 150mm? Although you won't find those exact lenses, but 85mm and 135mm are available; they just require a bit more cropping. One full frame option is a telezoom lens, such as 70-200.
A 35x zoom on a point-and-shoot camera almost certainly starts from around 30mm (35mm equivalent), and goes to aroound 1000mm (35mm equivalent). Thus, the zoom is way more than what you need. Excessive, I would say. Typically the superzoom lenses aren't the best in producing good pictures. They are just best in zooming in to such ridiculous magnification ratios that the image will be shaken so much that even the image stabilization can't correct it.
But the big question is, does a point-and-shoot camera take good enough pictures? You need plenty of light for such a small sensor. With the feeble flash, you can't have enough light. Thus, a tripod and asking the subjects to stay still is necessary for useful pictures, although image stabilization could perhaps in some situations be enough to not require a tripod. Image stabilization of course doesn't stop the subject movement.
A larger sensor camera such as APS-C DSLR / mirrorless is a much better choice, because it collects far more light and can render the background out of focus. You can find DSLRs very cheaply today, but the lenses require some investments. For portraits, do get 50mm and 85mm for APS-C. 50mm is very cheap, 85mm costs a bit more.
Of course, the ultimate portrait camera would be a full frame one, but I would say that is overkill for most uses.
