Yes, that is true. The problem is known as “stochastic singularity”. The problem is that in a linear model if you have fewer shocks than observables, there will be an exact linear combination implied between observables. That in turn means that the density of observing those variables is either 1 (the exact linear combination in the model holds in the data; rarely the case) or 0 (the exact linear combination does not hold; the typical case). As you can imagine with a log density of minus infinity, estimation will not work.