AFAIK, forms do not trigger an autoresponse at all, unless there would have been questions rissen with
DCL. They'll basically take the form as given and go with it from there. So if no questions, you'll never hear a word about it again, so to say. Or as we'ld say in Dutch; no news is good news.
A quick adding; the post below only is with regards to contacting the spec. needs desk directly as I no longer deal with the shore desk when it comes to my specific needs during the cruise.
Contacting them through email and/or phone? Let's see... the longest it took to get a response was about a day, which was a confirm of recieving the info I supplied about a specific aid that would need to be OK-ed by the onboard safety officer. That OK took about a week or so, I think. Was rather quickly.
All other things tended to be taken care of within 1 or 2 workdays, including the department actually calling me to discuss the email I sent. Spend like 30-45 minutes on the phone, considering I'm not from the US, considered it pretty

as I knew the biggest reason for them calling was to make sure things are OK and not wanting mailreply to cause confusions.
Quickest? Within 5 minutes after me calling the department they called me back. This was a call with me basically complaining/asking for help after having a

-experience with the regular shore desk and not being able to get a discount I was eligable for because I need an accessible stateroom. Already had one booked, but shore desk basically blew me off with a "no can't do because of the acc. stateroom", while they could've simply made a new booking under the discountcode, cancel old booking after transferring the stateroom. Within 5 minutes, the spec. needs desk not only hunted down the right person for this within shore desk but also already had the new booking made and in total it was a very simple experience. Saved me over $800,- on a then $2000+ rate.
So basically whether it being mail or phone, I've always gotten a rather quick to upright speedy response from them.