Translation of mRNA?
Yes, bacteria will produce human (or any organism's) proteins if you introduce their genetic material but there are a few things to consider.

First, the introns must be removed from the human genetic sequence. Bacteria do not have the machinery to splice out introns after transcription. This is typically done by using a viral protein to reverse transcribe mRNA, which already have the introns removed, into DNA which you can use to transform bacteria.

Second, you need to insert a Shine-Dalgarno sequence. This allows the bacterial ribosomes to bind to the mRNA they will produce, and translate the protein you desire. This sequence is not found in eukaryotic genes, so you have to make sure it was included either in the vector or in the PCR primers you used to amplify the gene sequence.