I did it with my instructor during my private training. He took off and got us into the clouds, then I got to try and hold level and straight. We were in and out. I got to make a 360 (with his help) and fly level and straight back to the airport. He did the ILS approach which wasn't that low at all, like 1000' ceilings and the FAF was above the clouds to boot. We didnt ask and I doubt we could have gotten a block of airspace considering where we were (busy airspace) north of west Denver. We were in and out of the clouds, which is typical around here. Not sure I'd call it a lesson, it was more of an excursion. I was happy just to get to fly in a cloud!
But if you are thinking about it now, some things to consider. The biggest is, a beginning student s likely to have trouble just holding straight and level. You can ASK for a block altitude, but ATC doesnt have to give it to you. Then what are you going to do? When you fly IFR, ATC tells you where to fly, and the pilot flies where told. MIght help to call ATC ahead of time and ask them where you might be able to get a block. Might be a long way away. They do have other planes to consider and cant always do it. Some ATC guys wont do it at all, I suspect. Some parts of the country are better for this than others. I know that some places have reliable 1000' ceilings, 1000' thick and you can get on top,then foggles above or whatever and do a real appoach through the clouds, albeit nowhere near minimums. Easy but good introduction for pilots in training. I talked to a guy from Michigan and he said its like that a lot there. Around Colorado, we are usually in and out of the clouds, getting on top etc, fighting high altitudes, ice and dodging T storms. Not often, maybe 1 day out of 20 you will find good, small plane flyable IMC. Best and most interesting IMC I ever found was in California. Like I say it varies, a LOT.
Frankly the idea is intriguing, but has a lot of pitfalls. Be careful and good luck if you try it.