My question is, on the pin VDD_1.2, what if I don't populate the 2.2uF and 100nF capacitors?
The two bypass capacitors have different roles. Every capacitor has internal inductance (often called leakage inductance) that affects the time-domain response of the (CL) capacitor-inductor to changes in the current drawn by an IC. In effect, the bypass device's CL is in parallel with all other devices on the board, through the power cables, and back to the power supply. The difference is that, being closer, this bypass device has less inductance on the PC, so the capacitance will be more effective.
The 2.2uf capacitor has more energy storage, so it can filter our a larger total energy change. It typically has a larger leakage inductance though, so the time-domain response of the CL is worse, and may allow a supply voltage dip that affects device operation.
The 100nf capacitor has less energy storage, but lower leakage inductance. It can more quickly supply or absorb energy.
Depending on how your PC was laid out and constructed, there is also capacitance between the power and ground nets of layers, which also provide a bit of filtering.
To analyze this, you should check the distance from the nearest alternative bypass device. If there is another 100nf capacitor "close" to the IC, you may be OK. If this is the only 2.2uf decoupling on the board, you may have a problem.
If you have a problem, you can expect random state transitions flip-flops, also known as state bits, in your IC. Even if your IC is purely combinatorial, you may get glitches in the outputs or slower propagation delays at seemingly random times. This can affect the setup and hold time requirements of subsequent inputs.
I see that this is an only EtherNet PHY. Most of the chips I've used are PHY/MACs, which have more state that can be corrupted. Even the naked PHY implements 32 registers of 16 bits which contain the device configuration.
There are many bits of state that can be corrupted.
Some of these will make the device inoperable until reprogrammed. Some drivers reprogram these bits frequently, and some program them only rarely, or even only once.
This PHY is probably connected to a MAC, perhaps in an onboard SOC.
Some errors result in packets being rejected, which as you noted, is not a fatal problem with ethernet. It will reduce performance. What is the packet timeout (retransmit time) on your network? With the standard specified values, a dropped packet results in a significant performance reduction, especially for TCP. What are your customer's expectations? Will they notice? If not today, might they later as the customer upgrades various parts of their systems?
Data from the PHY is passed to the MAC through an RMII interface. Does this interface meet the timing specs when the power does not? Probably not. Here the situation may be worse because some corrupted bits may result in corrupted data being passed to the system memory. What happens depends on the ethernet stack, and how careful it is about recomputing (at CPU expense) checksums. If the packet checksum was computed correctly, but the data was corrupted in the buffer, will the system use the corrupted data? What further errors will that corruption cause? Since we "know" the ethernet packet was correct, some drivers and protocol stacks will avoid a further checksum in the interest of efficiency.
Final thoughts:
One of my key rules of engineering: If it takes more than three sentences to describe why something works, it doesn't.
There is much that can go wrong. The process of determining which mitigations you have in place, and adding one you don't, is costly. Add those costs into your cost-benefit analysis when deciding if you need to write a recall, manufacturing deviation authorization, rework instructions, or whatever paperwork you have in your shop. Your name will be associated with the decision. Costs today are quickly forgotten. Recurring problems, loss of company reputation, canceled orders, negative reviews -- these don't have a chance to be forgotten and will stay with you.
Make things right for your customers and your company will grow.
You can even turn this into a positive PR statement, either to customers or at least in your internal communications, to build your quality reputation. Every company makes mistakes. The good ones fix them.
Addendum:
A few days after I wrote this answer, a friend sent me a link to an article about a company in a similar situation -- manufacturing had not built the board with the right set of components, but the board (nearly) worked as required. This company informed its customers, and is building both better internal processes and an external reputation for responsible, quality engineering. Here is the link: Another consequence of supply shortage: mass production mishaps