Honesty in Employment Data
It is not advisable to hide, lie, or fudge data to any employer, whether it's salary or any other information. Every organization has policies around hiring and background verification checks. Organizations definitely conduct background checks, which cover employment-related proofs (i.e., last designation, year of employment, character/behavior during the service, salary checks, etc.), present or permanent address verification, academic verification, criminal checks, etc.
During background checks, some organizations may not reveal the salary information, but this does not apply to all employers, as there are many other ways to verify these details. My advice is not to fudge any data, be open, and gain expertise to earn good money. I wish you all the best for your future endeavors!