if the primers have been properly well designed, the first step in PCR cycles is a hold that de-hybridizes double stranded nucleic acids, DNA or RNA. so yes, it should work and give you the waited amplicon.
The previous step to run RT-qPCR is to perform retrotranscription, where the viral retrotransciptase synthesizes cDNA from your total RNA. This means that you can find the cDNA analogous sequence of different classes of RNA, being this mRNA, miRNA, among others. There should be no problem to amplify a miRNA that was previously bound to an mRNA, even if it were bound yo AGO or Dicer-1, theoretically, due to the range of temperature used while performing the protocol, The corresponding cDNA should be synthesized by retrotranscriptase and, indeed, amplified by PCR polymerase.
I think if you want to estimate miRNA expression the regular qPCR won't work (which we are routinely doing for gene expression).You have to use specific kits for RNA isolation (miRNA isolation kits) as well as miRNA amplification specific kits where they use U6 as normalization control and 3' universal primers.
I agree with Poonam, of course you will need the 3'-end primers to specifically isolate miRNA, wich happen to have a distinctive composition. If you go after total RNA retrotranscription, there' s a big chance that the enzyme will bias to retrotranscribe higher concentration transcripts, yielding in low number of miRNA copies.
All the answers from other members are really good, hope you got the answers about what you wanted to know.
I also have similar views like Poonam Pandey said,
-You can even isolate total RNA using Trizol method and use Qiagen miScript II RT Kit, which converts all miRNA in a sample to miRNA cDNA and then use those cDNA directly for qPCR to check the miR level itself as well as other GOI.