TL;DR - unless you’re extremely ill or badly injured, you’re probably not getting taken to hospital at all.

It really depends on your situation. Assuming you get admitted, it’s not the first (or second) thing they do unless you’re wet and have hypothermia, or your clothes are at risk of injuring you (like if you’re in tight trousers and have a broken leg that’s swelling) or they need access to an injury.

If you have a condition that makes you pass out for a short period of time and then come around spontaneously, or there’s an easy treatment (like sugar for diabetic hypos), chances are you won’t be admitted at all, and might even recover before an ambulance gets there. As overpacked as hospitals are, you’re unlikely to get admitted unless there’s something specific that needs to be done for you that can’t be done at home. If the paramedics decide you need to be taken to hospital, you still may not actually get admitted, but be held in the waiting area and then sent home if you seem OK. 

Without knowing specifics of your condition it’s hard to guess either way, but my experience with paramedics - both first-hand and as a carer for a mother who had them called out quite a bit in the last few years of her life - is that once the ambulance gets called to your situation, unless it’s a clear emergency (like a stroke or heart attack) it typically takes 45 minutes to an hour for them to run initial tests and decide whether to take you in at all (and which hospital to take you to, which takes quite a bit of liaising with other people; they don’t just decide on their own unless you’re in a very rural area with only one hospital) and most of the time they’ll decide you don’t need to be in hospital. They’ll likely see if they can wake you up, test your blood sugar with a finger prick, test your oxygenation and heart rate with one of those devices that goes on your finger, maybe run an ECG, look at your phone to see if you have any medical details on there. (I suggest putting info about your condition into the health page; on iPhone this is viewable even with the screen locked, though I’m not sure about Android.)

In the last seven or eight years I think we had them out maybe ten times, and only three of those times required hospital trips. The three that did were hypothermia (after getting dumped in a river in January), sepsis, and end-stage COPD with difficulty breathing - which did result in a hospital admission and eventually death five weeks later. Ambulance calls that did not require hospitalisation were several accidental falls (one that included broken ribs), a few episodes of dizziness and fainting, suspected heart attacks that turned out to not be heart attacks, diabetic hypos that caused fainting. Each time they were clear that it was good that we called them, because it might have been something that required a hospital trip, but ultimately it was treatable at home.

Passing out would normally not require a hospital trip unless it’s accompanied by something else, like indications of severe infection, severe heatstroke or dehydration, a head injury, a lot of blood loss, maybe something that shows up on an ECG. Most likely they’ll check you over, make sure you’ve got someone you know with you (call them if necessary), maybe suggest something to drink or eat, probably suggest a visit to your GP tomorrow.