It really depends. In wireless communications, it's often the case¹ that the majority noise is actually happening in the receiver – which is why you'd want a low noise figure on your receiver. So, there's usually no "broadcast static" – the majority of that noise power happens in your receiver, not on the air. Many receiver architectures will increase the sensitivity if there's no strong (intended) signal in the air, leading to amplified noise, too.
In these bands, the pure presence of an increased noise floor would give away the presence of a broadband interferer.
Now, things aren't quite that easy in general: Whilst a single "non-jammer" interferer usually isn't white in spectrum as what you describe as "static" would usually be, a sufficient number of summing interferers with random properties would both be white in spectrum and gaussian in amplitude distribution, making the detection of your jammer harder.
However, receivers with multiple receive paths cannot be deceived: Your transmitter would be detectable to transmit from a single direction, and thus, if you, for example, add up the signal from two antennas with just the right phase, you could isolate your transmitter well, because they constructively add with that phase, but cancel out with other phases. That technology, both in receive and transmit direction, is called Beamforming, and it works with any signal (note that the receiver noises in both receive paths are independent and never add up constructively, whereas the artificial jamming signal is correlated on both antennas). It's basically a form of triangulation. You can also do the same with distributed antenna systems that coordinate their observations in a central point, so that you can do trilateration.
On large scale, that belongs in the category of things that you'd typically do to do radio surveillance for signal intelligence, airspace security, or cellular infrastructure coordination. So, that's broadly employed wherever there's industrialized areas.
So, if you try that, especially with high TX power, prepare for a visit from your local regulating body, asking you very nasty questions. It might be a criminal offense, depending on which bands you interfered with and where you are.
¹ HF, if I remember correctly, being the most prominent exception