Can PCR detect phosphorylated protein?
No. PCR (and quantitative PCR, or qPCR) rely on primers. They will amplify DNA flanked by primer regions, and this 'multiplied' DNA will be detected (and quantified).

PCR can be used to detect DNA. Reverse transcription followed by PCR (RT-PCR) can be used to indirectly detect RNA. Neither method is used to detect protein abundance, or post-translational protein modifications such as phosphorylation. This is because the modifications are not inherently encoded* in the nucleic acid sequence. They occur only on the protein level. Also, the abundance of a transcript tells you very little about how much protein will actually be produced from it, and how long this protein will remain in your biological system. A single mRNA can result in two very differently-modified proteins, and PCR would not be able to distinguish between an mRNA producing one kind or another. Also, phosphorylation is often a temporary modification, it's good to remember that.

*unless you have transcript variants (that produce protein isoforms) which omit or gain sequences that are modifiable, in the environment of a specific biological system.