Can I get away with multiplexing an array mechanical Relays via Mosfets?
Yes, it's doable.

Rather that what you call a "tiny delay" it's the %age on that is a major limiting factor.
For example, a tiny off delay of 100 uS will not allow the relay to operate if the on time is 1 uS.You need to say how many relays you have in mind and what sort of "activity" you have in mind. 1000 or 1000 MOSFETs, all toggling at sub second rates, is quite a different 
task to say 16 relays which switch at typically 1 per second.

In the latter case above you can use simple multiplexer ICs (such as the CD4051 with a mall capacitor on each MOSFET gate allowing the MOSFET to be used as a sample and hold.

And, if you want impressive and retro 50's methods, you may be able to do the latter task with diodes only, or even just port pins and some resistors and maybe diodes. 

So - please better define your need and we can better assist you.



CD4051 sample and hold.

8 relays. 4 port pins. 1 x CD4051.
CD4051 is configured as an 1:8 mux.
3 port pins provide address to 1 of 8 outputs.
Outputs drive FET gates.
Gates have small cap to ground.
CD4051 input is switched high or low by 4th port pin.
If high, selected MOSFET is turned on.
If low, selected MOSFET is turned off.
That is only a 2:1 gain over using 8 x port pins.

16 relays may be drive with 5 lines and 2 x 4051.

Special magic may allow 16 port pins &amp; 2 x 4051 to drive 64 relays.

A capacitor will help but may not be necessary.