Improve GPS accuracy by disabling cellular data
Cellular has nothing to do with GPS - they are two distinct technologies.  So disabling cellular will not increase/decease the accuracy of GPS

I thought the GPS partially relied on cellular data to improve its
accuracy.

Cellular location data can augment GPS to improve the performance of location tracking (where you are), but it can't improve the accuracy of GPS.
There are four basic technologies that provide location data:

WiFi location data
Cellular location data
GPS (GPS, GLONASS, Galileo, and QZSS
iBeacon (Apple centric Bluetooth Low Energy)

Focusing on WiFi positioning, cellular positioning and GPS, all of them work in tandem to get your position.
Your iPhone location sensor (Broadcom BCM4774) is the receiver that GPS uses.
Cell Phone Tracking
Basically, cellular location tracking is done at the cell cite - which antenna you're connected to; it approximates your location and augments it with GPS data.

A cell phone’s location can be detected through  cell site location
information (CSLI) or global  positioning system (GPS)  data.


WiFi Tracking
With WiFi positioning it takes a known quantity (the location of the associated AP) and measures the signal of the wireless client.

The most common and widespread localization technique used for
positioning with wireless access points is based on measuring the
intensity of the received signal (received signal strength indication
or RSSI) and the method of &quot;fingerprinting&quot;.


GPS
GPS uses multiple signals to measure location.  However, multiple factors like signal strength blockage, weather, etc. affect the signal.  Accuracy, however, depends on the quality of the receiver (the chip in your phone) and the number of signals it uses.

GPS is good down to the cm (centimeter range) and even down to mm, but to get this type of accuracy, it depends on the sensor being used.