The simple answer is no, not out of the box.
Though, you can potentially do this via a custom script that is triggered via task scheduler on the server itself. The script would look something like this. Here is the syntax for tabcmd. tabcmd Commands
for /F "usebackq tokens=1,2 delims==" %%i in (`wmic os get LocalDateTime /VALUE 2^>NUL`) do if '.%%i.'=='.LocalDateTime.' set ldt=%%j
IF %dayofmonth% LSS 10 (
GOTO END_PROC )
cd x:\Tableau\Tableau Server\your_version\bin
Another option would be to create a schedule for each day of the month (or from the 10th onwards) and then add each of these schedules to the workbook / Data source to be refreshed. (so that it has 20 odd schedules assigned to it)
Not sure that this is a better options than Jeff's though!!
Also, just checked out my Task Scheduler on my Windows 10 PC, and I have the following options re scheduling. This may also work, running a tabcmd batch file
All the best