The official spec says no not ever.

9020 MT/SFF/USFF/Micro  Technical Specification

Intel®  4th generation Core™ i7/i5 Quad Core (84W for MT / SFF, 65W / USFF 35W),
Core™ i3 Dual Core and Pentium® Dual Core (35W for Micro only)

The reason for this is basic

POWER SUPPLY

SMT   290W 90% Efficient PSU (80 PLUS Gold); Active PFC
DT    255W 80% Efficient PSU (80 PLUS Bronze); Active PFC
SFF   200W 80% Efficient PSU (80 PLUS Bronze); Active PFC
MICRO 065W Efficient PSU (80 PLUS Bronze); Active PFC

  
PSU: This form factor utilizes a more efficient Active Power Factor Correction (APFC) power supply. Dell recommends only Universal Power Supplies (UPS) based on Sine Wave output for APFC PSUs, not an approximation of a Sine Wave, Square Wave, or quasi-Square Wave (see UPS technical specifications).  If you have questions
please contact the manufacturer to confirm the output type

The PSU's for different sized units are listed in the 9020 spec sheet.

Hi,

I have seen a lot of the Optiplex 9020s SFF with i7-4790 CPU online. Like this one:

https://www.cnet.com/products/dell-optiplex-9020-sff-core-i7-4790-3-6-ghz-8-gb-500-gb/

Do they come with a different power supply compared to the ones with i5-4570?

Thanks

I did see the specs pdf. My question is that i have seen the same size OP was asking about ( SFF size ) come with both i5-4570 and i7-4790. Is there a difference in PSU between a SFF i5-4570 & SFF i7-4790?

Yes, you can upgrade to the I7 without upgrading PSU's.  Also, PSU's in the smaller units - DT on down (SFF included), are rarely ever upgradeable.  With that generation of Optiplex's and the generation before it, one needs to have an MT if they want to upgrade PSU's; exceptions are rare.

Since the original subject line had "I7-4790k," I wanted to iterate that's a no as Speedstep said.  It has an 88W TDP and the limit for the 9020 MT & SFF is 84W.  It would have to be an I7-4790 84W or I7-4790S 65W.

For what is worth, here is my experience so far: I just got (about a month ago) a used 9020SFF with an i7-4790. I installed a GTX 1050 Ti in the pcie x16 using a riser cable, using it for X-Plane 11, no problems whatsoever, even when overclocking the GPU.

I also recently purchased (waiting for delivery) a 315W PSU, just to be on the safe side. Said PSU even has a 6 pin cable for a video card, so I guess that moving besides the slot-powered 1050Ti might be an option.

I will leave the PSU oustide the case, and place the 1050 Ti inside, getting rid of the riser cable. 

To summarize, I would say that a 4790K will work without any problems with the stock PSU, but it would never hurt to upgrade the PSU to the 315W available in amazon. It's the same exact size, a real bolt on replacement. I will leave it outside just because I don't feel comfortable having the 1050Ti outside of the case.

I have seen some posts on the forum that are old, but it appears that some people did get 4790k to work.  What they didn't mention was if they had to upgrade the PSU or the bios.  I have an OptiPlex 9020 MT that I purchased with no CPU and RAM.  I have a 4790k and 16gb or DDR3 that I planned to use.  However, when I have them installed, system won't power on.  The orange led flashes in a patter that indicates memory / motherboard / cpu.  I am not sure if that means there isn't enough power going to the CPU and there fore won't work?  I'm sure the RAM works and even though it's been a while the CPU should be working.  Any suggestions or thoughts?  Thanks

I have just recently replaced Core i5-4570 with Core i7-4790k on my Dell Optiplex 9020 SFF. I also have GT1030 installed. No PSU upgrade but still works fine. So I would say it probably works for you as well.

Biggest concern will be the heat produced by i7-4790k. If your CPU is already pretty hot, it will be  dangerously hotter even if it works. I have resolved this issue by delidding and using liquid metal... which is of course not advised unless you know exactly what you are doing.