In most cases, no it wouldn't be blocked. That has been my experience as one who does the same. I was at one school that was incredibly restrictive in which only approved sites could be visited, but I assume that is fairly rare.
http://edublogs.org/ is a good one to try. It was designed with teacher/student blogging in mind. Teachers create, manage and moderate student accounts, as well as specify students' level of access (roles include administrator, editor, author, contributor and subscriber). http://www.classblogmeister.com/ was developed specifically for classroom blogging. Blog accounts are established and maintained by the teacher. More information, their terms can be found here: http://classblogmeister.com/conditions_sl.php
While blogging "in house" is safer since outsiders can't read and participate, you also decrease the authenticity of participation. You eliminate the ability of students to interact with experts on a particular subject. And while moderation will prevent inappropriate comments it also decreases spontaneity. Imagine your classroom if your students had to first whisper in your ear what they want to say so you could approve whether or not they could make their comment out loud. That is essentially what moderation is. You wouldn't do it in a class discussion "in person", why would you do it online? I tell teachers to treat blogs the same as you would class discussions.
I just found out about edmodo, and am becoming more convinced that it is offering everything that I wanted to EASILY connect with my students and keep parents in the loop (because there is the option of making posts public). I had previously tried a variety of things to get everything that I wanted out there -- this is by far the easiest and most common sense! I would highly recommend checking it out!
As Jerry suggested, 21classes.com is a great site. Students have to be approved by their teacher in order to create an account on the class page. It is very easy for teachers to monitor as well. Hope this helps!
I have played with Edublogs, and 21 Classes. However, I was immediately hooked on Kidblog because of the quick set up and I had to do virtually no training/practice with my 4th and 5th Graders. Easy to set up classes, easy to monitor. Does not have any bells and whistles, though, and visually not as interesting. But if you have younger kids that are just starting, it is a great start and they LOVE it!
I have just been using Kidblog with a group of 6th graders - love the simplicity. The teacher I was working with was relly impressed with how easy it is and the ability to see what they post immediately.
My own blog is on Edublogs and I used to push teachers towards it. However, all the features that made it so appealing (bulk management of student accounts) became a "pay for" feature and that turned me off. At this point Kidblog is free, extremely easy to set up and manage. The teachers in my district are only beginning to look at blogs and the Kidblog platform has what they tend to look for. We have asked Kidblog if they have any plans to create a "teen"version - what high school student wants to use KIDblog? Their response was positive so perhaps in the future they will have a similar platform geared for older students.
I use 21classes.com and like the customizability. My students like customizing their layouts. It is a completely closed blogging community, but can be public if the teacher chooses. Comments can be moderated or not. You can only have 10 free student accounts, though, which is a drawback. It is also a bit glitchy. For example, when you change the banner, background or profile picture, it reverts all the colors back to the default. Great if you're going to change your theme, but not so great if you just want to update your profile picture.
I just discovered kidblogs.org and signed up for an account to check it out and compare to 21classes. It is similar to 21classes in format and controllability, but much simpler to use. This is because the layout is not customizable. The background and blog pages are identical for all students. The dashboard is simple and easy to use (not always the case with 21classes), and it's completely free. I may consider changing to this free option next year and forego paying for the 21classes blog. You may want to check it out and see if it will meet your needs.