Well, interesting enough crossover. I keep hoping we'd see more Hellsing crossovers set in the 30-year timeskip period at the end of manga, with Integra and Seras keeping things from falling apart, but apparently Alucard is just too popular with writers. No real clue about timing on the Hellsing side of things yet.
Now, from things said in first chapter, I'd place the time in Dresden Files between Small Favor and Turn Coat. A few reasons for this. First, Harry remarks it's been a few years since the Zombie fiasco. Secondly, he mentions the war with the Reds just evened out in their favor recently, which is consistent somewhat with White Night and Small Favor, since things took a decidedly not-in-their-favor turn in Turn Coat. So before that, probably. What this means is that Harry has most of his late-game goodies already, pretty much everything bar the Mantle. And Molly has been at this for a while also.
Now, to look at the critter side, Dresden's Ghouls and Zombies vastly outperform their Hellsing cousins, in all but reproduction. On the other paw, most Hellsing vampires that even marginally deserve the name outperform the majority of Dresden-side's vampires until you get into the high ranks. And in those, Dresden side's ranks go way the hell higher. To consider, the leaders of the Red Court, the Lords of the Outer Night, are comparable to minor gods like Odin. And these are not really at the top of Dresden's cosmic hierarchy in the long run. Against these, the White Council of Wizards managed a years-long war from a bad position, because while they lose in numbers, their quality makes up for it. Consider that Morgan, a super vanilla combat wizard well into his second century, with no external power boosts, very nearly killed that comparable-to-a-god Red King on the field of battle. The vampire only survived because it managed to run away.
So with that kind of throw weight, even against the likes of Hellsing, the White Council is not exactly something to take lightly. And considering they are headquartered in Britain, I find it implausible in the extreme if they don't know about Hellsing and their type of vampires, if they in fact exist in the same universe. Harry is also on pretty good terms with members of Vatican's church, including the Knights of the Cross, which would be a big deal in a combined world. Also, Michael would probably be the very definition of a 'Real Human' by Alucard.