Yes, it is possible. I can't see any problem with this type of analysis, but care should be taken with the gene IDs. You have to keep the fasta format, so I recommend you to edit each sequence header as:
>org1_gene1
acgatcgat
>org1_gene2
cgatcgatc
>org2_gene1
cagtcagt
>etc
With an easy to read fasta file you shouldnt have any problem to multiple align those seqs. ^_^