Yes, it's pretty much at the location's discretion, but you need to read the terms and conditions of the upgrade carefully. Here it is for Avis/Budget:
Coupon valid for a one time, one car group upgrade on an intermediate (group C) through a full-size four-door (group E) car. Maximum upgrade to premium (group G), excluding intermediate SUV (group F). The upgraded car is subject to vehicle availability at the time of rental and may not be available on some rates at some times. All taxes, fees (including but not limited to Air Conditioning Excise Recovery Fee, Concession Recovery Fee, Vehicle License Recovery Fee, Energy Recovery Fee, Tire Management Fee, and Frequent Traveler Fee) and surcharges (including but not limited to Customer Facility Charge and Environmental Fee Recovery Charge) are extra. Fuel charges are extra. Coupon valid at participating Avis locations in the U.S., Canada, U.S. Virgin Islands and Puerto Rico. One coupon per rental. Coupons cannot be transferred, sold and we reserve the right to change terms anytime at our sole discretion. A 24-hour advance reservation is required. May not be used in conjunction with any other coupon, promotion or offer. Upgrade will be applied at vehicle pick-up time. Renter must meet Avis age, driver and credit requirements. Minimum age may vary by location. An additional daily surcharge may apply for renters under 25 years old. Rental must begin on or before 6/30/22.
And this is for Enterprise:
Free Upgrade: Valid on reservations made for an economy through standard size car at standard daily or weekly rates at participating locations in the U.S. and Canada. The upgraded car class will not appear on your reservation but will be applied at no extra charge upon arrival at the rental counter if a car in the next higher class is available. A minimum one-day rental is required, and a 27-day maximum applies. Enterprise, the “e” logo and ‘We’ll Pick You Up,’ are registered trademarks of Enterprise Rent-A-Car. #169 2017 Enterprise Rent-A-Car.
In short, the maximum upgrade with Avis/Budget is to a premium car if you booked a full-size car. With Enterprise, the maximum upgrade is to a full-size car if you reserved a standard car. SUVs and other vehicles are always excluded from the upgrade offer, but you can always ask.