Hi musicman9434,
That will depend on whether you have a box spring (that flexes) or a foundation (that has limited or no flex), its age and condition, and on whether it would be suitable and meet the warranty criteria for the mattress you buy. There is more about the different types of foundations and box springs and other mattress support systems that would generally work best with different types of mattresses in the foundation post here but if it’s a “cheap” box spring then the most likely answer would be “probably yes”.
Phoenix