Probably, but why would you want to? That data would be reported in the company's EDGAR filing, or 10-K/10-Q or whatever, whether you want it to be published or not. Not that they would have your private info in it, but the transaction itself would be a matter of record.
Different question but how is physical certs transacted in the USA? Do I just get the certs re-registered at the transfer agent then release funds once confirmation comes through? I've done for Canadian stocks but never for US stocks.
The question is does this sale of physical stock certificates also pertains to a sale of the stock ownership itself or is it just a sale of the actual certificate itself but with no change in stock ownership? As far as I know, the registration of trades on stock exchanges is only for recording of any changes in actual stock ownership via transactions in the stock in the primary and secondary market. If this sale of physical stock certificates also pertains to a sale of the stock ownership itself then yes, it will result in the registration of the sale of the stock, not the sale of the physical stock certificate in NASDAQ. If it is just a sale of the actual certificate itself but with no change in stock ownership, then no, the cash sale would not need to be recorded on NASDAQ because in this case, you are just selling an ordinary item, a piece of a paper certificate. And with any sale of ordinary items, the transaction would just be recorded in the GDP. To count the transaction also in the stock exchange would be double-counting.