I would not put them in if they have bloomed, let alone gone all the way to seed. In theory if you turn a pile often enough and get the mix of carbon to nitrogen right and get the moisture right, the seeds will cook. The reality is that you are not going to achieve that unless you use one of those barrel composters and work at turning, getting the right mix of carbon to nitrogen, and keeping moisture levels right. In a pile on the ground you are not going to get everything in the middle to cook.
If they have not bloomed, yeah, toss them in.
The things you should avoid putting into compost is obnoxious weeds because of the seeds and diseased plants from your garden. If you have a heavy insect infestation check out how those insects overwinter. Some overwinter in the plant debris so don't add those infected plants to your compost. You are not supposed to add cat or dog poop either, supposedly since they are carnivores they can add some potential disease organisms. I'm not worried about a little of this poop but I avoid large quantities.
Some people say not not add meat or grease. These can draw flies or critters that dig through your compost. I do add some of this but when I do I bury it deep and I have a cover to put over mine to keep critters from digging it up. It does need to be buried deep.