We expect batches to be produced quickly, on the same order of magnitude as current CT logs - somewhere in the 0.5s to 5 second range. This is an existing problem since (at least some) CT logs do the same batched behaviour.
Now, there is a catch with MTCA: That gets you a "standalone" certificate, which works just like a certificate does today. But it's big, still. To get the new, small certificates (landmark-relative), you will have to wait for the next landmark. Based on current planning and discussions with Chrome, we expect that to be hourly for short-lived certs, and 4 hours for longer-lived certificates.
So you'll get a big cert instantly, but you might have to wait an hour or 4 to get a certificate. So your new website can be online quickly, but with some downsides until you get the small landmark-relative cert.
(I work at Let's Encrypt)
If this fear of yours is particularly poignant, I invite you to share it with the forum so they have it in writing. It makes it easier for them to consider it as they work on a solution.