What will happen if your unit doesn't have funds to send soldiers to ALC?

1SG Patrick Blue's answer should help you, but additionally, it's all about how your DTS (Defense Travel System) Operator routes the approval process. DTS in a sense, the military's version of Expedia to book lodging, transportation and other incurred Costs during business travel, only difference is DTS allows the routing of who funds those costs... Yes typically when a unit sends soldiers to training they would have to use their units LOA (Line of Accounting) to pay for all of the incurred costs, however as 1SG mentioned, NCOES is MTSA (Military Training Specifc Allotment) funded, in fewer words.. Big army pays for it, not the unit. It is alarming how much those put in the position to run DTS do not know the difference between LOAs or cross organization funding codes... etc. Also most units S-3s schools sections (traditionally) run DTS for schools, however it is on the traveler/soldier to initiate a authorization/itinerary of all of the proposed costs, get in the JFTR (Joint Federal Travel Regulation) to see what is and isn't covered in your travel, could be the difference between you being authorized a rental car for your trip versus taking your POV and being reimbursed for mileage.

NCOES is not paid by the unit when I attended ALC the SGL's explained this to us.

If your unit is using that as an excuse then they are full of it; could be they don't want to send whoever they are saying that to in order for them to keep the spot open for someone else.