All semis are more PRONE to this phenomenon because of their inherent resonance,compared to a solid body - but it varies model to model, etc.
i'd guess if you want a semi you'd be into blues/jazz/rock n roll? and you'd probably find that with MOST amp settings for that kind of music it should be ok..try one and see.. go into the shop in the week, when it's quieter and try to play it on higher gain settings..wake the dozy buggers up for a start..and also see if it feeds back much.
Congrats on the Tele one of my favourite weapons - if she was owned by a 'Yes' guitarist it may be worth putting her in the att..WHAT am i sayin' a Tele is for playing with/on,use it in good sonic health.
Accuracy,you say? hmm interesting concept..