No. You can manually edit text to change its case but Word Online can’t change the case of selected text at the click of a button the way the desktop application can.
If you have the Word desktop application, click Open in Word to open the document and change text case there.
Tip: We're continually updating Word Online based on input like yours. Tell us how we could improve this feature for you. At the bottom of the Word Online window click Help Improve Office.
Vote for an idea, or share a new one in our suggestion box at word.uservoice.com.