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You can always implement signing yourself, though, without relying on somebody else's infrastructure. Just include the public key in the app itself and use it to verify your updates are properly signed by your private key before accepting them. I haven't checked but assume/hope Signal is doing this with their updated JS packages.
If none of this were to happen, however, then the answer to your last question is "yes", though with a caveat: If Signal's servers are compromised and push out a malicious update, then all bets are off, as the app running on your system has access to all your unencrypted messages. If the compromised server is only one of the messaging/relay servers, however, things are not as bad, as they don't have access to your keys and thus can't decrypt your messages. They can still forward them somewhere else for later decryption, but thanks to perfect forward secrecy this is currently rather unrewarding.