The simplest models of inflation predict small non-Gaussianities and a featureless power spectrum. However, there exist a large number of well-motivated theoretical scenarios in which large non-Gaussianties could be generated. In general, in these scenarios the primordial power spectrum will deviate from its standard power law shape. We study, in a model-independent manner, the constraints from future large-scale structure surveys on the local non-Gaussianity parameter f(NL) when the standard power law assumption for the primordial power spectrum is relaxed. If the analyses are restricted to the large-scale-dependent bias induced in the linear matter power spectrum by non-Gaussianites, the errors on the f(NL) parameter could be increased by 60% when exploiting data from the future DESI survey, if dealing with only one possible dark matter tracer. In the same context, a nontrivial bias vertical bar delta f(NL)vertical bar similar to 2.5 could be induced if future data are fitted to the wrong primordial power spectrum. Combining all the possible DESI objects slightly ameliorates the problem, as the forecasted errors on f(NL) would be degraded by 40% when relaxing the assumptions concerning the primordial power spectrum shape. Also, the shift on the non-Gaussianity parameter is reduced in this case, vertical bar delta f(NL)vertical bar similar to 1.6. The addition of cosmic microwave background priors ensures robust future f(NL) bounds, as the forecasted errors obtained including these measurements are almost independent on the primordial power spectrum features, and vertical bar delta f(NL)vertical bar similar to 0.2, close to the standard single-field slow-roll paradigm prediction.