This forum can help with you routine issues, but not outliers as many people may not have seen such situations. Also, outliers with Indian consulates ... what more to say.
Anyway, here's what could happen.
a) they return the application to you within days
b) it keeps sitting with them
Here's what you could do:
a) talk to them and figure out the process which works best for you ... return and resend, or hold and wait for you to send additional docs
b) send the additional docs anyway giving the reference of the application already sent. however, in the absence of a tracking number (i do not think it is there for SC as you do not fill it online), it is probably not going to work.
there might be other scenarios which might happen. the options i see are wait (anyway you still need to apply for us passport), send the docs anyway (iffy), or chase them (painful).