In short, the answer is no. See citations below for the explanation. Note: bold – italics added for emphasis.

IAW FAR 30.000 “...This part does not apply to sealed bid contracts or to any contract with a small business concern (see 48 CFR 9903.201-1(b) for these and other exemptions)."

FAR 9903.201-1(b) The following categories of contracts and subcontracts are exempt from all CAS requirements:

FAR 9903.201-1(b)(3) Contracts and subcontracts with small businesses

Nowhere in FAR part 30, DFARS part 230 or FAR Chapter 99 (48 CFR 99) is there any authority for the Contracting Officer to deny the exception and require the small business concern to submit a disclosure statement. This is a serious requirement as evidenced by the approval threshold for any individual or class deviation on this matter (see DFARS 201.402(1)(iii)).

Now... if you wanted to challenge the size standard of the company in question, that guidance is found at FAR 19.302. But I highly encourage you to discuss this with your Small Business Representative or Professional and Contracts Legal office prior to seriously looking into this option... should you choose to.