Neck dive is when your guitar's headstock feels heavier than the body, meaning you have more weight in your fretting hand, and your headstock “dives” towards the floor when you let go of the guitar instead of staying in a playing position.
Do Les Pauls have neck dive?
In a standing position, with the strap end about 3 or 4 inches out along the shoestring from the strap button, the Les Paul will feel like an entirely different guitar. No neck dive. No body dive.
Can a Telecaster neck dive?
Tele's are simply not a practical body shape to avoid neck dive. You want something with a longer upper horn. That said, you can always opt for the lightest tuners available, possibly even going for a graphite truss rod.