No. For a number of reasons. First of all, the virus uses the nucleotides (A, G, C and U, for wich Ψ is used as a substitute) produced by the attached cell to create a copy of it's genome (RNA). The nucleotides are produced by the cell, the virus does not instruct the cell to produce them. It just tells the cell to produce and assemble the proteins AND the RNA.

Second, our immune system doesn't just attack and recognize free floating RNA, but the virus itself. And different parts of the virus. First and foremost it will recognize the surface proteins (like the spike protein) because those are the things that it can see while the virus is outside of the cell. Also these are the things that the infected cells present on their surface (MHC II sites, if I'm not mistaken) to the immune system. (As far as I can understand, cells have to present the proteins they produce to the immune system otherwise they get killed. If they produce alien virus proteins that get recognized by the immune system, they also get killed.)

Interesting enough, the immune system somehow also recognizes the so called nucleocapsid protein, which is the one used to wrap the viral RNA inside the virus. (But it gets produced by the cells, so I guess they get presented on the cell surface so the immune system can learn to recognize and counter them.) I didn't look into the details too much, but as far as I can understand it's not clear yet how those antibodies (the ones created against this protein) work, because antibodies are supposed to be used outside of the cells, but the nucleocapsids are only present inside the cells and then inside the virus.

To sum it up: the immune system is much more complex, has several recognition mechanisms, the viral RNA is mostly packed into the viruses (or are inside the cells) and the viruses don't have any way to produce Ψ (or any of the other nucleotides).