Yes, planets near a black hole or neutron star would experience gravitational time dilation due to the intense gravitational fields in their vicinity. According to the theory of general relativity, the stronger the gravitational field, the slower time runs.
If there were inhabitants on such a planet, they would indeed notice the effects of gravitational time dilation, but the extent of the effect would depend on the specific conditions. For example, if the planet is orbiting a black hole or neutron star at a relatively large distance, the time dilation would be relatively small, and the inhabitants might not perceive it in their everyday lives.
However, if the planet is located very close to the black hole or neutron star, where the gravitational field is extremely strong, the time dilation would become more pronounced. In this case, the inhabitants would experience time passing more slowly compared to observers in weaker gravitational fields.
The effects of time dilation near a black hole or neutron star would manifest as a noticeable difference in the rate at which processes occur. Clocks on the planet would run slower compared to clocks in regions of weaker gravitational fields. For example, if there were synchronized clocks on the planet and elsewhere, the clocks on the planet would fall behind the clocks in the weaker gravitational field over time.
In extreme cases, such as being very close to a black hole's event horizon, the time dilation could become so significant that it could have dramatic consequences for life on the planet. Time could pass much more slowly on the planet compared to distant observers, potentially leading to substantial differences in aging rates and the perception of time. However, reaching such close proximity to a black hole or neutron star would pose immense challenges for the survival of any life forms due to the extreme gravitational forces and other harsh conditions in those regions.