In chemistry, scientists tend to not publish failed results whether it is a synthesis that fails, or an organism that have been studied for its chemistry and showed no bioactivity or novel secondary metabolites. Journals simply wont publish such uncitable results. However, if you end up getting good results when you publish them, you can say in the process we tried other plants/synthetic routes and found nothing interesting.

Maybe try turning it around. If there is a plant you wish to work with, do a literature search to see what has been purified from this plant already.

I've seen many papers where novel compounds have been published, but no biological activity has been found as yet for them.

For example, this paper mentions biological activity for related compounds, but the isolated compounds haven't been been tested as yet: Article Tremorgenic Indole Diterpenes from Ipomoea asarifolia and Ip...

Quite a lot of work has been done on compounds from specific plants e.g. thyme. If you type "composition of thyme essential oil" into Google Scholar it will give you pages of results and many of the papers deal with the biological activity of this oil and/or its individual compounds. So it depends on the plant and the compound. So often it is not that the work hasn't been done, more about finding it. Of course there will be many plants where no work has been done so this may not be much help. If you try searching for the chemical composition of a plant extract/essential oil you will often come up with any work which also looks at biological activity (if there is any). If there isn't, then there is your next research project. As far as I know there is no centralized database containing this information. It would be huge as there are so many plants which have been or are being analysed.