Here is some info for you to digest…
NEC (2017) 840.49 addresses metallic entrance conduit grounding for premises-powered broadband communication systems, including twisted pair:
Metallic conduit containing communications entrance wire or cable shall be connected by a bonding conductor or grounding electrode conductor to a grounding electrode in accordance with 800.100(B).
800.100(B) is lengthy and lays out a lot of requirements, but the key bits are that the GEC for your conduit must be 14 AWG or larger, as short/straight as possible and less than 20 feet, and connected to some part of the existing GEC system, generally.
800.48 is also relevant. If your cable is unlisted, you are limited to a 50 foot span once inside a building but may extend inside using IMC or RMC.
800.48 Unlisted Cables Entering Buildings. Unlisted outside plant communications cables shall be permitted to be installed in building spaces other than risers, ducts used for environmental air, plenums used for environmental air, and other spaces used for environmental air, where the length of the cable within the building, measured from its point of entrance, does not exceed 15 m (50 ft) and the cable enters the building from the outside and is terminated in an enclosure or on a listed primary protector. The point of entrance shall be permitted to be extended from the penetration of the external wall or floor slab by continuously enclosing the entrance cables in rigid metal conduit (RMC) or intermediate metal conduit (IMC) to the point of emergence.
Informational Note No. 1: Splice cases or terminal boxes, both metallic and plastic types, are typically used as enclosures for splicing or terminating telephone cables.
Informational Note No. 2: This section limits the length of unlisted outside plant cable to 15 m (50 ft), while 800.90(B) requires that the primary protector be located as close as practicable to the point at which the cable enters the building. Therefore, in installations requiring a primary protector, the outside plant cable may not be permitted to extend 15 m (50 ft) into the building if it is practicable to place the primary protector closer than 15 m (50 ft) to the point of entrance.
BUT FROM YOUR ORIGINAL QUESTION!!!
I hope this was a joke…
“Rigid metal conduit, which is the ground path, so it contains no wires at all.”
Do not do that!!!!!!!!!!