Lauren Ambrose is not in that league. Though I'd love to see her do some musical some time, "Funny Girl" as an entire show isn't good enough to be carried by strong acting and a loud belt alone. I'm not sure if you've ever seen her on stage, but to my mind, Ambrose is probably the most captivating stage actress of her generation. When she is on stage, your focus can be nowhere but on her. It goes beyond just "strong acting," as you put it, and I think it's a quality that is absolutely necessary for Fanny. As for the voice, she does have an incredible belt (I've heard her belt live, in a small space, and am convinced she could blow the roof off the largest Broadway house there is), but she's also focused a lot of her technique on jazz singing and has developed a unique style in her voice. There are any number of young belters who can walk on stage and throw off "Don't Rain on My Parade" or "I'm the Greatest Star" without the slightest hint of subtlety, but there are very few who can actually perform the role with the right amount of coloring it needs. Hypothetically speaking, I'd put Ambrose in that category.
I think BillyBoyA and Henrik hit the nail on the head: Are we expecting someone to play Fanny Brice, or to play Barbra playing Fanny Brice? If you want the latter, hire a drag queen. This to my mind is one of the main reasons the show has gone without a major revival for 50 years.
(And again, as we clutch our pearls, let's remember that this is a very unsubstantiated rumor. I doubt that the OP will return to name his/her source.)
"You travel alone because other people are only there to remind you how much that hook hurts that we all bit down on. Wait for that one day we can bite free and get back out there in space where we belong, sail back over water, over skies, into space, the hook finally out of our mouths and we wander back out there in space spawning to other planets never to return hurrah to earth and we'll look back and can't even see these lives here anymore. Only the taste of blood to remind us we ever existed. The earth is small. We're gone. We're dead. We're safe."
-John Guare, Landscape of the Body