Could 2 synchronised RX chains be used to receive a signal too wide for just one of them? Say the goal is to demodulate a "wide" signal, e.g. 300 MHz wide. An SDR is available with a maximum RX bandwidth of 150 MHz (ADC sampling freq. limitation), but it comes with 2 RX channels sharing the same clock source.

The proposed approach is connecting the same antenna to both RX chains. Ideally, they would take the same clock source, but one ADC would trigger on a rising edge and the other on the falling edge of the clock, thus effectively doubling the ADC sampling rate and allowing downstream demodulation logic to correctly demodulate a 300 MHz signal.

If this is practically doable, what are the constraints (w.r.t. SDR analogue RF frontend capabilities, compensation for loss of signal strength due to splitting it into 2 RX inputs etc.) and if not, why not?
In lack of more background, I can only give a general answer:

What you describe is simply an interleaved ADC; that is a technique employed in very high-rate ADCs. And high-rate definitely is more in the range of hundreds of MHz, not a mere handful! For your proposed rates, cheap ADCs can directly sample sufficiently fast. In fact, in the context of SDR, you'll find that most ADCs used are actually doing higher rates on two simultaneously sampled channels in order to allow IQ signals to be meaningfully digitized.

So, yes, that is possible, but it's incredibly hard to do well-synchronized and balanced enough. Just get a single sufficiently fast ADC. In fact, I'm not even sure what SDR-centric ADCs you're looking at that these rates become a concern at all.