Is it possible to use if...else... statement in React render function?

There actually is a way to do exactly what OP is asking. Just render and call an anonymous function like so:

render () {
  return (
    <div>
      {(() => {
        if (someCase) {
          return (
            <div>someCase</div>
          )
        } else if (otherCase) {
          return (
            <div>otherCase</div>
          )
        } else {
          return (
            <div>catch all</div>
          )
        }
      })()}
    </div>
  )
}

Not exactly like that, but there are workarounds. There's a section in React's docs about conditional rendering that you should take a look. Here's an example of what you could do using inline if-else.

render() {
  const isLoggedIn = this.state.isLoggedIn;
  return (
    <div>
      {isLoggedIn ? (
        <LogoutButton onClick={this.handleLogoutClick} />
      ) : (
        <LoginButton onClick={this.handleLoginClick} />
      )}
    </div>
  );
}

You can also deal with it inside the render function, but before returning the jsx.

if (isLoggedIn) {
  button = <LogoutButton onClick={this.handleLogoutClick} />;
} else {
  button = <LoginButton onClick={this.handleLoginClick} />;
}

return (
  <div>
    <Greeting isLoggedIn={isLoggedIn} />
    {button}
  </div>
);

It's also worth mentioning what ZekeDroid brought up in the comments. If you're just checking for a condition and don't want to render a particular piece of code that doesn't comply, you can use the && operator.

  return (
    <div>
      <h1>Hello!</h1>
      {unreadMessages.length > 0 &&
        <h2>
          You have {unreadMessages.length} unread messages.
        </h2>
      }
    </div>
  );