Will a nucleic acid sequence deduced from a protein sequence be expressed from a plasmid?
I lack the knowledge to fully answer your question but I can give some potentially useful pieces of information:

In theory you can easily in-silico reverse translate a peptide
sequence to an unambiguous nucleotide sequence using the GMOs
optimized codon usage. I can share a Python script for that.

Also you could easily search for the 'real' nucleotide sequence in
databases. For example use 'Blast' to find the gene of your peptide
sequence.

But attention! There are known cases of codon-optimized sequences
causing bad protein folding or even (paradoxically) worse expression
levels than the native sequence.

There is software that helps with the design of plasmids, also in
light of use of unique restriction sights, helping to decide which of
your restriction enzymes are applicable.