Due to limited bandwidth and high delays in access to Smart Meter measurements, it is not possible in most cases to access measurements from the complete set of smart meters in a low-voltage grid area for distribution grid monitoring. Distribution system state estimation can be performed based on measurements of voltage and active and reactive power from a subset of selected smart meters. Increasing the number of selected smart meters will, on the one hand, increase the accuracy of distribution system state estimation, while on the other hand, it will degrade timeliness of the monitoring data. This paper proposes to utilize part of the idle time of the legacy periodic smart meter data collection for access to measurements from the subset of selected smart meters for distribution system state estimation. It subsequently proposes a methodology on how to quantitatively analyze this trade-off. The methodology is applied to an example LV grid area with 20 customers using a weighted least square state estimation with support of pseudo-measurements obtained during the regular smart meter collection cycle.