Not really following the path you describe, but SER cable can be installed exposed under the floor. I can tell you, if there are any bends in the conduit you want to install, you will have a difficult job pulling the #4/0 SER cable through it.
So your question, does the SER need to be in conduit from the floor into the load center, does not describe where the SER would be exposed.
If the SER will only be exposed 30 feet, with the remaining being in conduit, you may want to consider pulling individual conductors.
Get back with more detail if you need more help.
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