No, it would not
First, deleting the partition changes no bytes on the drive outside the partition table. All of the original directory and file structure remains on the disk.
Second, even if other allocated blocks are overwritten by file data, data will be easily recoverable from the last assigned block,
Third, even a full Ubuntu load is smaller than a full Windows load with equivalent applications. Think of all that now-unused space where Windows used to store data.
We used to think a full format that wrote F6 to all bytes on the drive was sufficient to protect our data. We now know we were wrong; with modern data recovery procedures and techniques, data can be recovered going back several write-overs.
