In CMOS, can I assume the delay of a multiplexer is negligible compared to the delay of an inverter

Logic gates get faster when the supply voltage increases. What you call the "time constant" of the charging path, isn't constant: it depends on supply voltage. If you think of it as an \$RC\$ circuit, the capacitance \$C\$ remains roughly constant, but \$R\$ decreases with supply voltage (remember that with increased \$V_{GS}\$ on a transistor, its resistance goes down), so \$RC\$ goes down.

A more accurate way to think of it is this: the voltage swing increases with supply voltage, so to maintain the same speed the charging current should also increase with supply voltage (remembering the capacitor equation, \$t=\frac{CV}{I}\$). However, for MOSFETs in saturation, the charging current increases roughly with the square of supply voltage (remembering the MOSFET equation, \$I_D=k(V_{GS}-V_{TH})^2\$). Thus, the time spent charging goes down.

This is true up to a point: once the transistors get small enough so that they no longer follow square-law behavior (because of velocity saturation), the logic gate speed no longer improves with increased supply voltage (because the charging current no longer scales with the square of \$V_{GS}\$, but instead scales linearly). Thus, for the latest process nodes, don't expect to improve speed by changing the supply voltage.

The typical PV installation is either classified as "off grid" or "on grid".

The off grid version charges batteries from the solar panels via a DC bus and an inverter converts the DC bus to AC to supply the facility loads. There is no interconnect between utility company provided mains and the solar system. These systems are often used when utility company energy is not available or it is prohibitively expensive to install and operate.

The on grid version is the most common form. Here a number of solar panels are wired in series and connected to an inverter. The inverter converts the DC bus from the panels to AC. The inverter monitors the utility company AC line and syncs its frequency and phase to the AC line. If the AC mains fail, the inverter has protection circuits so that it drops off of the AC line to avoid causing harm to power line workers, etc. Many installation codes still require a separate mains disconnect switch, however. This type of system supplies all of its energy back to the power utility and the facility loads remain connected to the utility. This essentially allows the solar produced energy to offset the purchased energy.

An on grid system can include any number of inverters to reach the desired energy capacity. No special connections are required as they are typically paralleled on the utilities side and connected to a unique string of solar panels on the DC side.

Either style of system can employ MPPT (Maximum Power Point Tracking). This is a technique that extracts the maximum power available from the solar panel under the current sunlight conditions. Some newer systems put small MPPT trackers in place for every solar panel or a small collection of panels with the promise of further optimizing the total solar panel array power when some panels are shaded by a tree or cloud for example.

A few on grid system offer an accessory connection to the inverter for a few kW of power to provide a limited form of backup for the facility when the mains fail. This is rarely sufficient to power all facility loads.