No, you can't. Because security is a key pillar of Neo, it will not allow third parties to install applications through an app store or through .(X)APKs
It does come with the following built-in applications:
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Whiteboard
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Wireless sharing (Airserver)
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Chromium browser (if checked during setup in the security options).
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Screenshot tool (via CTOUCH button/Quick menu).
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Annotation tool (via CTOUCH button/Quick menu).