When the question is "is it possible to sue X over issue Y?" the answer is always "Yes". Anyone can sue over almost anything, and some people will. Some suits have almost no chance of success, adn some will be dismissed promptly. But even so, they can cause trouble and some expense for the defendant.
In this case, it seems that the developer, who is also the copyright holder, has granted others the right to read the source code, but not to download it or run it. The developer (whom i will call D) has not asserted that the code successfully performs any particular function, and has not sold or delivered it to any particular customer or user.
None the less a reader R does download the code, compiles it, and runs the resulting binary, thereby arguably infringing D's copyright. R finds the code not to work as R had expected, and R sues D for damages on an implied warranty theory. Could R win such a suit?
Well this may depend on the particular laws of the country or jurisdiction where R brings suit, and the question does not specify that.,
In the US one possibly relevant law would be the Magnuson-Moss Warranty Act of 1975 ut this act applies only to "written warranties on consumer products costing more than $10." As D makes no charge for the code, and provides no warranty at all, the Act weill not apply to D.
The page "Be Wary of Warranties for Software Design " from Jones Day discusses the California Commercial Code and the Song-Beverly Consumer Warranty Act. The Act imposes an implied waranty if there is any express waranty. The page reads:
Implied Warranty of Fitness for a Particular Purpose
This implied warranty comes into play when the software supplier knows of the buyer's particular purpose for purchasing the software and knows that the buyer is relying on the supplier's skill and judgment to provide suitable software.
Since there is no purchase here, this does not seem to apply.
The Jones Day page also reads:
Implied Warranty of Merchantability
This implied warranty, as its name suggests, promises that the software meets the standards of performance expected by merchants in the trade. Again, this implied warranty turns on industry standards and practice. Suppliers can disclaim this implied warranty or agree with purchasers to particular terms that will supersede it.
Disclaimer of Implied Warranties
Unless prohibited by the Act, the Code allows sellers to disclaim any express and implied warranty. Software suppliers may decide to provide a limited, exclusive, and express warranty (such as meeting a particular specification or industry standard) and then disclaim all other warranties. Disclaimers must be specific and conspicuous; state law and practice provides the important language and format for disclaimers. If the Act applies to a transaction, for example, the disclaimer must say that the goods are sold "as is" or "with all faults."
I see no obvious legal theory on which a suit for an implied warranty could be successful against D, but I have no way to know what provisions the law of R's jurisdiction might have.
Including a disclaimer such as:
This code is posted for demonstration and discussion only. No right to download and run it has been granted. It is provided "as is". The author makes no assertions as to its performance or effects if run, provides no warranties of any kind, and disclaims any implied warranties.
costs nothing and might deter some people from filing suits, even if such suits are unlikely to prevail.
