Not automatically. Levels are connected to paragraph (styles). InDesign has no inline-paragraphs as Frame Maker would have. So you have to have for each level a dedicated paragraph with its paragraph style.
You can do it with an "Apply Next Style" in the first paragraph numbering.
When you hit return it can trigger the Next Style - of the different numbering list in a new paragraph style.
I would do it a little differently.
You're going to need as many paragraph styles as you have Arabic numbers in your list.
Set the paragraph style for numbers for the Number field as 1.)^/^#.^t
This gives you a static number 1 followed by a period, figure space, number (formatted with letters), period, tab.
Then create a second paragraph style with the numbers as 2.)^/^#.^t
Continue with a paragraph style for as many Arabic numbers.
You can then use a keyboard shortcut to switch from one paragraph style to the next when you need to go up or down the list.
Whoops, I just realized you don't need both the ) and the period for the starting number. Choose whichever one you do want.
Thank you all, specially Sandee :-)