Yes, you can use a vertical antenna, but it's not ideal. There is a null overhead. They will work better on lower elevation passes. If the vertical is on an HT, you can hold it sideways to receive on a high elevation pass.

There are omnidirectional antennas for satellites such as a quadrifilar helix or turnstile antenna that will work very well for stronger signals like the ISS and the old NOAA satellites.

@JackbyDev @AG7LR
I bet you could. Here are the pictures I received during the autumn experiment.
The cheap Quansheng UV5-K8 radio with custom firmware and whip antenna Nagoya NA-771 (which is most probably non original) were used.

I noticed you have the RTL-SDR blog dipole. I've used that for NOAA-APT and Meteor LRPT in the past just fine. 120 degree V shape helps with impedance.

Handheld you can also adjust for elevation. Half wavelength (around 1m) above ground will work for most passes, but bringing it lower increases gain towards the top (held horizontally).

I never learned NEC, so I can't prove it to you.