You won't have local caching. However, this is no issue at all, since the caching will be done for you in the Pi-hole now. Even on a Raspberry Pi version 1 the answer should arrive your client within at most 5 milliseconds, so I highly doubt you will ever be able to notice the difference.
It is just not good to don't have DNS caching at all, so that is why Ubuntu enables it via default (since there isn't a Pi-hole in every household).
For a while I was happy, but today I was hit out of nowhere by the same problem again, local domain names are no longer resolved. A a ping gives me the following output:
ping borg
PING borg.fritz.box (127.0.53.53): 56 data bytes
On my client runs macOS 10.12.4 (I have tested it with Arch on the same client too, same result). I have nothing changed on my configuration. It is pretty weird.
EDIT: After a Fritzbox firmware update it works again - the question is: How long?
Might I ask this question after nearly one week?
Sure @DL6ER, it seems I did a very stupid mistake, I have setup a second Upstream DNS server, which led to this weird inconsistent behaviour 
.