star trek - Do ships at warp experience time dilation?

From the Gene Roddenberry quote in this answer:

'In answering these questions, I came up with the statement that "this time system adjusts for shifts in relative time which occur due to the vessel's speed and space warp capability. It has little relationship to Earth's time as we know it. One hour aboard the U.S.S. Enterprise at different times may equal as little as three Earth hours."'

Hold on a second, is this a reference to relativistic effects? Time dilation? Do ships at warp even experience time dilation? (I'd assumed the special-ness of subspace travel prevented this.) Are there any in-universe references to a crew at warp experiencing a different duration of time than people who are stationary (say, on a planet or in a station)?

Answer

From Wiki:

Warp drive is a faster-than-light (FTL) propulsion system in the setting of many science fiction works, most notably Star Trek. A spacecraft equipped with a warp drive may travel at velocities greater than that of light by many orders of magnitude, while circumventing the relativistic problem of time dilation.

However, Wikia contradicts that with a more authoritative, if detail-less reference:

In "The Cage", Captain Pike orders the Enterprise to travel at "time warp, factor 7". Instead of traveling through time he simply refers to the normal warp factor. According to Star Trek Maps, the word "time" in that context is only a reference to the normal time dilation that occurs during all warp travel.

However, Memory Beta contradicts that with the reference to a book (which is not canon).

Since spacetime itself is moving and the starship is not actually accelerating, it experiences no time dilation, allowing the passage of time inside the vessel to be the same as that outside the warp bubble. (ST novel: Captain's Blood).