There's nothing Alucard can do to knock Wolverine off of his game. I think one of Alucard's best tricks is his ability to freak people out by morphing his body or releasing some hell hounds. Wolverine has seen too much shit (and survived a couple of trips to various hellscapes himself) to be knocked off his game by this.
I think both would end up being on their top game for this to be honest. Alucard would see Wolverine as highly skilled and someone worth fighting. Wolverine's prepped 24/7 for killing so the mind games really don't come into play here.
Alucard also doesn't seem to be the world's greatest shot, especially when it's a target that's actively trying to avoid being shot by him. Allucard has very powerful guns, and while it would be impossible to shoot of a limb like he's capable of with human opponents, the gun could certainly provide impressive stopping power and possibly KO Wolverine if he nails enough head shots. But I don't think he has the sharpshooting abilities to land head shots on a guy who will be actively trying to dodge or block them (and is more than capable of doing either).
I would disagree, Alucard has shown the ability to connect with a head shot from a very long distance away. The difference is he's always fought enemies that have super human speed. Alucard's guns do not fire any faster than a normal gun would, so those that are fast enough can avoid the bullets.
So for this instance, Wolverine does move at super human speed, so yes he can dodge the bullets. Alucard moves at super human speed as well so it's about reflexes and positioning. Both are phenomenal warriors so this could be a fantastic chess match between the two of them dodging and attacking.
The only question I have is how does Wolverine end Alucard? I have no doubt that he could chop him into pieces, but can't Alucard recover pretty quickly from that?
This battle is pretty much what Alucard vs. Father Anderson was. Anderson is a regenerator who can heal from pretty much anything, uses a multitude of blessed blades to cut Alucard up, and Alucard regens as well. They were fairly evenly matched in terms of speed and ability. In their final battle Alucard ripped Anderson's heart out to defeat him to make a long story short.
The difference is Anderson had a plethora of spells for a lack of a better term at his disposal to bind Alucard down allowing for a wider attack window as well as send a whirlwind of blades at him, of which Wolverine has no magic or mystical abilities at his disposal. Even with Anderson's blades blessed, they didn't do anything of particular other than slashing or stabbing damage to Alucard. Wolverine is going to cut up Alucard but it's not going to end up doing much.
Actually, here's another question: will being in a church do anything to debuff Alucard?
Nah he's actively walked inside churches with no issues. He's used his own dark composition to melt a blessed silver cross down to be used a single bullet against Incognito in the original series. His own weaponry is blessed and has Christian imagery on them.
This isn't going to be a match that ends in death, only a KO, unless Alucard blows Wolverine up enough that he can devour him, though still not 100% sure on how Adamantium would react to the dark composition. That's going far too deep down a metaphysical argument with no basis for information.
I think it boils down to Wolverine can only hold out so long before succumbing to injuries. Wolverine has been knocked unconscious in the past, and has also collapsed from taking too much damage, effective enough for a KO, and with explosive rounds it should be enough to cause concussive damage at the very least. It's not going to be a short fight by any means of the imagination. They're going to battle for a long time, though as you said J, I don't think Wolverine has anything in his arsenal to do enough damage to keep Alucard down, nor is he going to be able to avoid every bullet sent his direction.
One final thing to note is Alucard does have the Dandy Man (or also known as Tubalcain Alhambra) who used razor sharp playing cards as weapons at his disposal as a familiar. These cards were shown to have a debilitating effect on regeneration abilities. When he and Alucard fought, the cards seemed to cause even Alucard difficulty regenerating from their damage. Since Alucard devoured him, he can summon him as a familiar and use those cards to either nullify or extremely slow down Wolverine's regeneration. Again, perhaps not enough to kill Wolverine, but enough to keep him down for the KO victory.
