Yes, a PC-lycanthrope can multiattack. Under any interpretation some of them do, and I argue that all do. (And you can skip to the last paragraph if you don't need to see the argument.)
Like you said, The PC-lycanthrope gains all of the abilities that don't involve equipment. A very strict reading would say that any action-paragraph that mentions equipment isn't imported: under this reading the wereboar and wererat import Multiattack just fine, but the other lycanthropes all don't import Multiattack.
This reading is too strict to make sense. It has the effect of making some afflicted with lycanthropy faster and able to multiattack (e.g. wereboar), but some not (e.g. werebear). This, even though all monsters with lycanthropy can multiattack.
Contrast this with a reading in which each portion of an action-paragraph is evaluated against "involves equipment."1
The effect of this reading is that the PC-lycanthrope gains natural attacks and the ability to multiattack, but doesn't gain any equipment.
A few examples, all quotes from the 5e MM pp.208-11:
A wereboar gains Tusks, doesn't gain Maul, and Multiattack reads as-is:
Multiattack. The wereboar makes two attacks, only one of which can be with its tusks.
A werebear gains Bite, Claw, doesn't gain Greataxe, and Multiattack can be read like:
Multiattack. In bear form, the werebear makes two claw attacks. In humanoid form, it makes two greataxe attacks. In hybrid form it can attack like a bear or a humanoid.
A werewolf gains Bite, Claws, doesn't gain Spear, and Multiattack reads like:
Multiattack (Humanoid or Hybrid form only). The werewolf makes two attacks: one with its bite and one with its claws or spear.
But even this is a little too much lawyering for me: note that the wereboar or werebear both get to make multiattacks that involve weapons, but the werewolf doesn't. Why? Because we're over-thinking it.
The action is the bold-italic word or few words: the paragraph that follows just explains it. (See also AngryGM's article on abbreviating stat-blocks.2)
Under this philosophy a PC-wereboar gains Tusks and Multiattack. A PC-werebear gains Bite, Claw, and Multiattack. And a PC-werewolf gains Bite, Claws, and Multiattack. I then understand that wereboar can attack with tusks and a weapon, but not twice with tusks. Werewolves can attack twice--one bite and one that somehow uses the hands--but the PC didn't gain a were-spear when afflicted.
1 - Note that for all of the lycanthropes in the MM, the only actions that do mention equipment are those relating to their (artificial) weapon attacks.
2 - Be warned that AngryGM's posts are liberally sprinkled with profanity and/or rude language. Nothing you might not hear on television, but still worth knowing before you innocently head over there.
The infobox makes it seem that loss of character control only happens if the PC embraces the curse and the DM chooses to take control of the character, and therefore simply not embracing the curse would suffice to keep the character as a lycanthrope complete with powerful boons like damage immunities but without any drawbacks. However, the lore earlier in the lycanthrope chapter suggests that the condition is impossible to resist during full moon:
A lycanthrope can either resist its curse or embrace it. By resisting the curse, a lycanthrope retains its normal alignment and personality while in humanoid form. It lives its life as it always has, burying deep the bestial urges raging inside it. However, when the full moon rises, the curse becomes too strong to resist, transforming the individual into its beast form --- or into a horrible hybrid form that combines animal and humanoid traits.
(from Monster Manual, page 206, under Curse of Lycanthropy)
Even a character that resists the curse is unable to control their bloodlust during full moon, as is traditional to werewolves in fiction. Ask your DM to keep track of the phase of the moon while you're infected so you know how fast you need to get a remedy or other countermeasures.
Best Answer
No. They need to Hit.
I think you're reading too much into wounding. There's no reason I can think of, in terms of defined game terms, to think that wounding refers to damaging vs. hitting. In other words, the rules don't tell us to prefer one over the other. In general.
However, flip back a few pages: "Player Characters as Lycanthropes" says, in part
There it is, as you first described: the save against cursing is part of the "Hit" clause and comes into play whenever a bite hits, even if it hits for no damage.
Some have expressed concern about what hit points represent, and whether a zero-damage hit is an injury or not. That way lies madness, I think, and we don't need to go there as Hit is a defined term.