"Does English allow..." is a problematic question, as English has no authoritative body to allow or disallow anything. As an attempt to provide a standard, several bodies issue "style guides", among the most influential of which are The Chicago Manual of Style, The MLA Style Manual, The MLA Handbook, and The AP Stylebook. They each have different histories and target audiences, so different editors and publications choose different ones for their own reasons. So to answer your question with authority you would need to consult the relevant style guide. For most purposes (writing that is neither academic nor journalistic) I use the Chicago Manual of Style.
As a general rule, though, (and according to the Chicago Manual of Style as I understand it) parentheticals should not be as long as a paragraph, and would typically be converted into a footnote instead. In some kinds of publications, they would be margin notes or endnotes.
If you just wanted to be ornery, you would probably follow the rules for including multiple paragraphs inside double-quotes and repeat the left parenthesis at the beginning of each paragraph, like this:
See The Chicago Manual of Style, 16th edition, Section 13.30, for how to quote multiple paragraphs.