Yes, there are a lot of studies describing the presence and identification of pseudogenes in bacterial genomes. And yes, pseudogenes can be analysed in qPCR with pseudogene specific primers.
as Abhijeet Singh mentioned, primers can be designed for gene/pseudogene specific amplification at the only condition to design primers in sequences different from both templates. those differences must be at 3'end of primers. If not possible because differences define long fragment, try to design lonPCR primers and use amplicons as template for second PCR with right length.