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.