Yes you can but for that you have change code in your ajax cart Jquery code and if you can't you have to hire some one because its little difficult process fro you.
Let me know if you can't
Please share the url of your site, what theme you are using ?
Okay, I got it, I am not sure it is possible to provide all details what to change via this forum, there is need to change theme.js file for ajax update and also the header for static update. it is about 30mins work to finish
at least 2 files
header.liquid and theme.js
The first one for static state, when the cart.item_count is via liquid, the second one for ajax update.
In theme.js you have to write a script to get cart items count after product added into cart, because in venture theme there is not such script already written.
Also will be need to edit styles to adjust the look of count, because for now it is just a cycle.