EDIT: I re-read your question. You asked if it was appropriate to ask, I didn't directly answer that. I'd go ahead and ask, with the backup plan of an inter-departmental team in my back pocket for the inevitable 'no', after all, what are all the other devs doing? Have they asked? What happened to them? 'Appropriate' is much harder to answer than 'what will happen'. 'Appropriate' depends more on your workplace than your end goal.
Being a current sysadmin and having worked in a development group, I feel semi-uniquely qualified to answer this.
To start: it can't hurt to ask*, but the answer is 'no' with p<0.05.
Let's move on to why: Imagine you own a bus company. You have buses you need to maintain, and drivers that you hire, and then train and trust to drive your buses. Some of your customers take the bus to the park, some to work, and some use it to make out on, but all your customers use the bus in the same way. One day, one of your customers comes to you and says that the buses drive too slowly and volunteers to drive the bus himself. He is, in fact, Juan-Pablo Montoya, winner of both NASCA and Formula 1 races, so he is certainly qualified to drive. Do you let him take the wheel?
That is how your IT department will see you. They gain no real benefit other than maybe the devs not complaining as much and open themselves up to more problems as developers like to 'play' with their things, and sometimes break them if they decide to close a port that the internal proxy requires you have open, or create a BIOS password for their workstation (ask how I know this).
Additionally, the IT department is subject to political forces that unless you are a lead engineer on the dev team you are likely not even aware of. I remember one time someone came to me explaining that they needed unrestricted internet access and that it should be easier to attain. I told him that if he could convince the CFO why he (the requester) should have full internet access, while the CFO lacked it, I would grant him internet access (I do not know if he attempted this, but I do know he did not get what he was looking for).
Suggestion talk to your manager. Unless he is ego-maniacal or sadistic, it is unlikely he enjoys entering a password for you all the time (probably for accountability purposes). See if, when there is less pressure on the dev team, there could be a small cross-department (IT + dev) team working on improving internal structure. Maybe one of the devs wants to write a script to automate what the dev team needs to be done, or maybe the IT department could use someone to cook up some config files while they support other users who's printers are 'broken', but really the paper tray is empty.
*Unless you have an extremely vengeful IT department, in which case, yes, it can hurt to ask