How to analyze a RC circuit with Integrated Chip in Parallel?
So there are a few reasons why this is a bad idea. First of all, 48V will break this IC anyway, but even if you use a different IC it's still not a great idea.

First of all, because of the resistor in series with the power supply, your supply voltage will be varying with the current draw of the device. This is almost always bad. Your capacitor will smooth that out, but it's still bad. In order to create a delay of 500ms (you don't define what you mean by "delay", and in this circuit, the "delay" will be a capacitor charging curve, as opposed to a straight line between 0V and 48V which is what you presumably want), lets assume you want two timing constants worth of delay. This means your RC should be 250ms (ignoring your supply current for a moment). 

Lets assume you can tolerate a (very) generous voltage drop of 5V across your resistor, and your circuit only draws 10mA. This means your resistor should be at most 100 Ohms. In order to get a 250ms, your capacitor has to be 2.5mF. This is quite a bit, especially at 48V. The problem is that 10mA is just the maximum standby current at 15V. You don't know how much current it will actually take because:


The standby current can be anything, they just guarantee it will be less than 10mA at 15V
The current will increase as the voltage increases, as shown in the datasheet
This is just the standby current, and the actual current will also include the amount of current drawn by whatever your opamp is driving


This will lead to inconsistent and potentially unpredictable performance, which is bad. There is almost certainly a better way to do this, but we need to know more about what you actually want (you mention buck converters and PWM). I would recommend starting a new question with a description of your system as a whole, and what you're actually trying to do.