Can the server administrator browse date of the hosting based KVM Virtualization?

Yes, of course they can. Remember this one rule and everything will all make sense:

It's true! There is no "cloud." There are only other people's computers. Yes, the provider may waffle and say that "we don't have a lot of insight" or "we can't login on your behalf", but that's all rather comforting half truths that don't tell the whole story. Unless you're using volume level encryption, and only you hold the encryption keys, your data is just lying on a disk and can be accessed with trivial effort.

Do not trust the cloud. The cloud hates you, hates your data, and probably kicks your dog when you're not looking.

Yes, you can't hide anything from the ones who 0wn both the hardware and the software your VM runs on.

As a mitigating measure you can make accessing your data more difficult by ensuring encryption for data in transit and at rest, by using secure protocols such as https & scp instead of http & FTP and setting up encrypted volumes.

Selecting the right encryption (with ciphers that support forward secrecy) helps to mitigate the risk as well.

In reality you can only hope that simply nobody cares enough to about your data to make the effort, hope that the hosting company has enforced policies that prevent unauthorized curiosity by the staff and default settings that make that non-trivial as well and last that you are not suspected of doing anything that draws authorized scrutiny to your activities.