The other answer is correct that this won't directly affect the Windows operation of this device, but not for exactly the reason you'd suspect.
Some devices have firmware that is an EEPROM, so when you perform an update everything that uses it gets the benefits and any issues that may arise from an update. Your system's BIOS is a prime example, you can upgrade (and sometimes downgrade), but once you perform an update it sticks.
Other devices like the wireless card operate on a per OS basis with a just in time firmware loading/initialization. Wireless cards typically do this because there are different legal frequency bands for different countries and until the system loads the firmware the card isn't sure which to use. You could theoretically run two different firmware versions for one card between Windows and Linux or between multiple Linux variants, but keeping them in sync speeds up the initialization because it doesn't have to reload with the right version every time.
In your specific case there is a package called linux-firmware that contains the binary blob required to operate your wireless card. These aren't always installed by default because they are ”non-free” as in they aren't open source. Installing this package via sudo apt-get update; sudo apt-get install linux-firmware
on a wired connection should get your wireless working. If it says package not found try sudo apt-get update; sudo apt-get install linux-firmware-nonfree
as occasionally the package names change between versions.