I have inserted a gene in downstream to Ef1a promoter of my mammalian expression vector. Can I check the protein expression using any bacterial expression host? Or, will it only express in any mammalian cell line under Ef1a promoter?
No, it will not drive gene expression in bacteria since promoters work by recruiting specific proteins and the ones EF1alpha recruits are not expressed in bacteria, but in mammalian cells.
Some promoters can have cross kingdom activity (eg. baculovirus IE1 promoters work in insects, plants and mammals) but you would need a hybrid Shine-Dalgarno/Kozak sequence (eg. https://patents.google.com/patent/US6627436B2/en) before your CDS if you want protein expression. Also in there are any introns in your protein, the bacteria will not be able to form a mature RNA. I would suggest doing some PCR on the cDNA to see if your promoter is active in the bacteria being used.
Ef1a promoter is not suitable for expression in bacterial hosts, as mamlian cell and bacterial cell promoters are different and they work in different way in bacteria hosts typically use promoters like the T7 promoter or lac promoter, which are recognized by bacterial RNA polymerase. Mammalian cells, on the other hand, use promoters like the Ef1a promoter, which is recognized by eukaryotic RNA polymerase. you should use a mammalian cell line to assess protein expression under the control of the Ef1a promoter.
The T7 promoter is not recognized by bacterial RNA pols. It is recognized by an RNA pol produced by the T7 bacteriophage genome. Some bacterial strains and mammalian cell lines express the T7 RNA pol as a transgene.