No, they didn't
The NRA is a civil rights organization, and isn't capable of blocking federal research funding related to gun violence and gun control. That is the job of Congress.
Congress passed the 1996 Omnibus Consolidated Appropriations Bill, which contains the following language:
none of the funds made available for injury prevention and control at the Centers for Disease Control and Prevention may be used to advocate or promote gun control
This amendment was added by U.S. House Representative Jay Dickey (R-AR) and was approved by 104th Congress. The American Psychology Association, that was against the Dickey Amendment admits:
this language did not explicitly ban research on gun violence. However, Congress also took $2.6 million from the CDC’s budget — the amount the CDC had invested in firearm injury research the previous year —and earmarked the funds for prevention of traumatic brain injury.
From the CDC themselves, they note the Dickey Amendment does not block research/funding related to gun control/gun violence.
AR-13: Prohibition on Use of CDC Funds for Certain Gun Control Activities The Departments of Labor, Health and Human Services, and Education, and Related Agencies Appropriations Act specifies that: "None of the funds made available for injury prevention and control at the Centers for Disease Control and Prevention may be used to advocate or promote gun control."
Anti-Lobbying Act requirements prohibit lobbying Congress with appropriated Federal monies. Specifically, this Act prohibits the use of Federal funds for direct or indirect communications intended or designed to influence a member of Congress with regard to specific Federal legislation. This prohibition includes the funding and assistance of public grassroots campaigns intended or designed to influence members of Congress with regard to specific legislation or appropriation by Congress.
In addition to the restrictions in the Anti-Lobbying Act, CDC interprets the language in the CDC's Appropriations Act to mean that CDC's funds may not be spent on political action or other activities designed to affect the passage of specific Federal, State, or local legislation intended to restrict or control the purchase or use of firearms.