Is it possible to hide the recently viewed accounts list view (drop down) from my users?

You cannot customize the standard tab in that way. However, you could create a custom Visualforce Tab to replace it, to remove recently viewed list view:

(1) If you want to take that route, first create the following Visualforce Page:

<apex:page tabStyle="Account">
<apex:enhancedList type="Account" customizable="true" height="600" />
</apex:page>
(2) Next you need to create a Custom Tab for it. Go to Setup > Create > Tabs. In the Visualforce Tabs section, click New. Select the Visualforce Page you created from (1). Find the appropriate Icon. I would probably set the visibility to Default Off.
(3) You will now have two Account tabs, and so will want to hide the standard tab for all Profiles. To do so, go to Setup > Manage Users > Profiles > [Select Profile] > Object Settings >Accounts. Click Edit and change Tab Settings to Tab Hidden.