Correlation between DC & RF voltage gains
There is some relationship - in a single-pole circuit, more gain results in more gain-bandwidth. 
In RF we try to tune out the main capacitances, and the main issue becomes the gate resistance, which form a RC network on the input. This will limit the maximum frequency at which we can still achieve power gain. When we reach extremely high frequencies (tens to hundreds of GHz) days, maybe even weeks of design work goes into optimizing the connection of the transistor terminals on chip to the on-chip inductors. We want to have as large a feed network as possible to reduce the series resistance, but at the same time this will increase the capacitance.