You can always send your furniture regardless of your immigration status.
However, depending on the type and value of the items, you can pay import duties and taxes on your furniture. Relief is available, but it will take a lot of paperwork to claim it. It may also be necessary to provide some security against the import taxes for the duration of your stay. It is this process that links your import with your visa status.
The government message that the rules are detailed can be found here, and the shipping company can also give advice.
Note, however, that problems can arise if you stay on landing much longer than indicated. For example, if you declare a visit of one month and stay for six, the immigration officer will want to know on your next visit how you supported yourself. If you can not provide a watertight statement, the officer may conclude that you have worked illegally and denied you entry. Danger.