Can Bluetooth beacon be detected while it's in motion?
Barring externally designed limitations or strange relativistic cars, the main concern will be if the vehicles are close enough for long enough to establish a connection and communicate the necessary information.

Suppose car A is moving at speed \$\Delta v\$ relative to car B, your wireless device has an effective range of \$d\$, and the two cars are initially out of communication range. Then the time you have available to connect and communicate is:

\begin{gather}
t = \frac{2 d}{\Delta v}
\end{gather}

Typical passing speed might be ~10mph, and assuming your bluetooth device has the class 2 radio range of 10m, the time available is about 4.5 seconds. If we assume instead that \$\Delta v = 80mph\$, you have ~0.56 seconds. Whether this is enough time depends on your actual devices and the amount of data you need to send.