No, it is not correct in the very strictest sense.「汐」means evening tide, and the character is never used to just mean evening.
There's a suggestion that whoever came up with the meaning eventide thought it meant evening tide, but I can't confirm this.
The real story is slightly more complicated. Notice how [潮汐]{ちょうせき} (morning and evening tides) forms an exact analogous pair to [朝夕]{ちょうせき} (morning and evening); in fact, they're cognates in Old Chinese and have become homophones in Japanese. Naturally, this is because there is a tight association between tides and the time of day.
According to Zhengzhang,「汐」and「夕」were both /*ljaːɡ/, so we can view them as representing exactly the same word - that is, there was originally one word for both evening and evening tide, and the different kanji were used to provide the different nuances.
So, while eventide is not correct for the kanji「汐」, it is correct for the word that「汐」represents, which is the same word as that which「夕」represents.
A note on kanji usage: In Japanese,「汐」can sometimes be used as a generic representation of tide, in which case it is interchangeable with「潮」. The word(s) that both「汐」and「潮」represents in this interchangeable case is しお/うしお. However,「汐」shouldn't be used for morning tide, so「あさしお」should not be written as「朝汐」. The reverse isn't true due to Jōyō kanji standardisation:「汐」is not a Jōyō kanji, so「潮」has taken over the function of「汐」for the word(s) しお/うしお. This means that evening tide can be written as「夕潮」, and is the standard Japanese representation.