In general the answer is no - however Google do have the capability of remotely removing apps (i.e. Malware) from everyone's device as required, and if they do so they will provide you with a notification.
This was explained by Rich Cannings, Android Security Lead in an Android Developers blog post, back in 2010:-
... In cases where users may have installed a malicious application that poses a threat, we’ve also developed technologies and processes to remotely remove an installed application from devices. If an application is removed in this way, users will receive a notification on their phone.
Recently, we became aware of two free applications built by a security researcher for research purposes ... [a]fter the researcher voluntarily removed these applications from Android Market, we decided, per the Android Market Terms of Service, to exercise our remote application removal feature on the remaining installed copies to complete the cleanup.
... a dangerous application could be removed from active circulation in a rapid and scalable manner to prevent further exposure to users. While we hope to not have to use it, we know that we have the capability to take swift action on behalf of users’ safety when needed. ...
This was then used to remove 60 malicious applications back in 2011
On Tuesday evening, the Android team was made aware of a number of malicious applications published to Android Market. Within minutes of becoming aware, we identified and removed the malicious applications. ... But given the nature of the exploits, the attacker(s) could access other data, which is why we’ve taken a number of steps to protect those who downloaded a malicious application:
We removed the malicious applications from Android Market, suspended the associated developer accounts, and contacted law enforcement about the attack.
We are remotely removing the malicious applications from affected devices. This remote application removal feature is one of many security controls the Android team can use to help protect users from malicious applications. ...