yes... surely you can use astro byond with your Sony CRT TV...
but, you will be not noticed any different when you watching HD Channels..
the quality are same as SD Channels... I have test my astro byond with my old Toshiba Bomba CRT, and yes, they're no difference on HD Channels...
and HD channels will become letterbox...

May i know your CRT has Component input or not? If it does not have component input, you don't have any choice at all... you only can connect your CRT with composite.. because astro byond decoder did not have S-video and RF connection like older decoder...

My advice, if you only own CRT TV, better not upgrade to byond because again you will not noticed any different in HD channels... same as before...
But if you want to make future upgrade, carry on...