The IC-R3 has very poor sensitivity on the AM broadcast band. and I could
hardly get any radio stations on it, except for my one local.

Well, this worked for me.

I decided to buy 75ohm F connector to BNC connector, and hooked my R3 into the
roof antenna by simply screwing the antenna wire i(that I would normally use to
watch tv) nside the trailer to the connector and screwing the other end of the
connector onto the R3.

I did this to get better scanner reception on the VHF and UHF bands.

As expexted, it greatly improved reception on the VHF aircraft band and FM
broadscast band, among others.

But to my surprise, it also improved reception on the AM broadcast band and
shortwave bands (even though tv antennas aren't made for these frequencies).

I was able to get most all of the AM broadcast stations in the counties and two
counties away from me on the IC-R3 with this method.

Unfortunately, I later had to move back here and there isn't any roof antenna
here and I'm not allowed to put one up here, so I'm omnce again back to poor
reception on the AM broadcast band when using the R3.

But the tv antenna worked great from AM broadcast band through normal tv
frequencies.
I'm not sure how high in frequency the tv antenna would have worked on the R3.
I imagine that the tv antenna might not be good for 2.4 GHZ, but then again,
it might.

Would a regular tv antenna (on the roof) improve 2.4 GHZ reception?

That is, would it be better for recieving 2.4 GHZ than using the supplied rod
antenna that came with the radio?