No, you can't change the order of your widgets on mobile without affecting the widget order on your desktop. To give our users a more predictable experience, we've linked the two views, so you'll see the same number of columns on both the desktop and the mobile view. Due to the restricted screen size on mobile, you have to scroll left or right to see every column, but the order is the same for both.
Related article
For more information about changing the order of your widgets, read this support article.