These are only my ideas from my limited experience, but...
I'd say as long as you have a mead that has gone over 10% ABV at time of racking, don't worry about pasteurization. The alcohol should kill off anything wild at that point.
There may actually be advantages for freezing the fruit and then thawing it...the freezing and thawing process seems to break down the structure of the fruit (thus why thawed frozen fruit is mushy and fresh fruit is firm) and while that is unpleasant for eating, it helps the meadmaking process along, easier for the flavours to leach out and the yeast to get in there and do what they do. I think, at least.
As far as puree'ing and straining...I don't know. When I racked onto cherries in secondary, I mashed them with a potato masher, that was it. Mulberries may be similar to blackberries and thus have fibrous "hairs", so there might be benefit to pureeing and straining, but being a bit lazy, I'd be inclined just to mush up the thawed berries, and rack on top of the fruit. Or you could use a large fruit bag suspended in secondary (if you used a bucket, not a carboy). You may still get some "hairs" but the key will be to wait a long time for it to settle, and carefully rack once every month or two until it has cleared sufficiently.
My mulberry tree is still dormant I think...it came without any branches, just a big stem with roots basically. Hopefully when I get back from California it will have sprung to life, we'll see.
"For evil to flourish all that is required is for good men to spout clichés." - Hugh Laurie