The answer is no.
Using off brand or remanufactured inkjet cartridges does not void your warranty at all. It is actually the law that printer manufactures honor their warranty regardless of the ink you choose to use in your printer.
It is a myth that printer manufactured like to perpetuate since they stand to gain so much from keeping the myth alive.
The following federal law applies to these cartridges:
MAGNUSON-MOSS WARRANTY IMPROVEMENT ACT
United States Code Annotated
Title 15 Commerce and Trade
Chapter 50 Consumer Product Warranties
15 Section 2302
“(c) No warrantor of a consumer product may condition his written or implied warranty of such product on the consumer’s using, in connection with such product, any article or service (other than article or service provided without charge under the terms of the warranty) which is identified by brand, trade or corporate name; except that the prohibition of this subsection be waived by the commission if:
1) The warrantor satisfies the Commission that the warranted product will function properly only if the article or service so identified is used in connection with the warranted product, and
2) the Commission finds that such a waiver is in the public interest.”
Under no circumstances may any company or associate, salesperson or service technician deny you service or warranty work that would otherwise be covered under the warranty program.