Does working as a consultant on a contract basis qualify for employment verification in Thailand?

Contract employment is increasingly the norm. Many DTVERS are contract workers so you are ok.

Was in a similar position (yearly contracts). What I gave them

- payslips/invoices last 6 month

- previous year client contracts

- current year client contracts

- brief explanation what I am doing and since when

Got approved and no further documents requested

No, working as a contractor is OK. I got my DTV this way. However, my company wrote a letter addressed to the local Thai embassy stating my start date, my position, my job description, my average monthly salary etc. It was signed by one of the big bosses of my company. Embassies live old fashioned stamps on printed (and later scanned) documents. Just originally digital documents (rather than scans of printed documents) aren't much well received.