Apple Watch Cellular without an iPhone?

Yes.

An Apple Watch GPS+Cellular model can be configured with its own cellular service separate to that of an iPhone, though you still need an iPhone to set it up either by directly pairing them or through Family Setup.

click here ➜ Set up cellular on Apple Watch - Apple Support

and here ➜ Set up Apple Watch for a family member - Apple Support

But there is still an iPhone in the mix.

Apple Watch Family Plan

Set up Apple Watch for a family member - Apple Support

Set up a family member’s Apple Watch - Apple Support

Some limitations: Cannot receive SMS/MMS messages, as that depends on a fully paired iPhone. Messaging is pretty much limited to Apple's Messages, unless the messaging service provides an Apple Watch app. Alarms, alerts, notifications on the iPhone are not sent to the Apple Watch. Apple Pay via a credit card is not available. Also not available: Medications, respiratory rate, irregular heart rhythm notifications, ECG, AFib History, Cycle Tracking, Sleep, Wrist Temperature, Blood Oxygen, Walking Steadiness, Audiobooks, Camera Remote, News, Shortcuts, and the double tap gesture.

If this is for your Wife, then I can tell you that when my Wife got an Apple Watch I was able to send her messages, call her, use Walkie-Talkie (between our Apple Watches), that was not really possible before, because she either leaves her iPhone in the kitchen with her purse, or when out and about, cannot hear messages delivery sounds in her purse, or because of ambient noise.

But with an Apple Watch on her wrist, she always seems my messages, and answers my phone calls. It was a total game changer.

One last thing.

The GPS Only Apple Watch will do EVERYTHING the cellular model will do AS LONG AS the iPhone is nearby, where nearby is generally in the same moderate sized wood frame constructed home.

So if your Wife's iPhone is nearby, then she gets all the Apple Watch benefits, even if it is in her purse, or in the kitchen.

Things I do with my GPS Only Series 4 Apple Watch (my iPhone is generally in my pocket; but it can be on a charger in another room): • It tells time, date, day of the week • Every iPhone alarm, appears on my wrist, where you can acknowledge it, dismiss it, etc… • I like the iPhone 3rd party “Alarmed” app (http://yoctoville.com), for my alarms • Ring.com door bell can display a static image on the Apple Watch • Weather (this gets used a lot) • MyRadar 3rd party app will display radar image • MyRadar and WeatherBug 3rd party apps will send you weather alerts • Make/Receive phone calls • Make/Receive FaceTime audio calls • Use Walkie-Talkie to other Apple Watches anywhere on the planet • Silence phone ringing by pressing the digital crown (great for SPAM calls) • Send & receive iMessages • Send & receive SMS TEXT • Say “Hey Siri, 14 and a half minute timer” • Say “Hey Siri, remind me when I get home to do xyz” • Say “Hey Siri, message my wife/husband/Susan/George/etc…” • Say “Hey Siri, start Outdoor Walk” • Say “Hey Siri, end workout” • Say "Hey Siri, find my iPhone" • Say "Hey Siri, flashlight" • Use a 3rd party garage door opener app and device (such as MyQ) • You can check your calendar • Read your email • If you need to take an iPhone picture where you cannot see the screen, use Apple Watch Camera app as a view finder/shutter release • 3rd party Ocean's Tide app for beach visits • Hand washing reminder and timer • Unlock your Mac (I do this several times a day) • Unlock your iPhone when you are wearing a mask • Track your exercise and physical activities Since my Wife got her Apple Watch, we have been able to reliably iMessage each other, as she never keeps here iPhone on her person. If my Apple Watch was lost, stolen, or broken, I would order a replacement as fast as possible, as I would miss it so much.