No, a conservative figure to use for HDD spinup is 2A each. "IF" the controller can do a staggered spinup (one drive at a time) then you can factor for total current for drives as 3 x 1A (already spinning) + 2A to spin up the last one = 5A total, instead of 4 x 2A = 8A total for drives alone.
The fans are likely a negligible current draw relative to the rest, but you should allow at least 2A more on 12V rail for the mobo & CPU... so for 12V current alone that is 7A total with staggered spinup capability /and implemented or 10A total without, meaning best case scenario would be 7A * 12V = 84W for 12V alone. The Pico 90W is not enough either... your HDDs require more power than the rest does AND generally speaking it is not good to run a passive PSU anywhere near its peak rated load either for best lifespan, especially if it has electrolytic capacitors in it.
Granted, CPU won't be at peak power simultaneous to ALL the HDDs spinning up so in reality you can shave a couple amps off but call that a minimum margin for good/long life. If you don't care about long life and you have staggered spinup you might barely get away with using the PICO PSU (or might not, drives with fewer platters and 5900RPM or lower (or SSDs) use less power to spinup) but is it really worth the risk to chance it for a server?
I recommend you use a plain ol' mATX12V PSU. That will also give you less downtime should the PSU fail later as it is easy to source a replacement locally if you can't wait for online order/delivery.
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