Since you didn't provide a picture, or a very helpful description of what you're looking at. I'll try answering your question by explaining how the switch itself works, which will hopefully help you understand the problem better.
Single Pole Single Throw (SPST) Pull Chain Switch
The pull chain switch that controls the light(s), is a single pole single throw (SPST) switch. It has two positions ON (Closed), and OFF (Open). Drawn simply, it would look something like this.
![Quarter turn switch (Closed)](https://i.stack.imgur.com/KfmZ7.png)
Switch shown in ON (Closed) position.
When the switch is in the ON (Closed) position, current is allowed to flow through the switch, through the light(s), and back to the the source (via neutral).
![Switch Closed Current flows](https://i.stack.imgur.com/GaAkb.png)
When the chain is pulled and released, the internal contact rotates 90° (1/4 turn) into the OFF (Open) position.
![Quarter turn switch (Open)](https://i.stack.imgur.com/u7E3N.png)
When the switch is in this position, current is not allowed to flow through the switch, and the light is not lit.
![[Switch Open Current does not flow](https://i.stack.imgur.com/2oXXC.png)
This is why the pull chain switch that controls the light(s) only has two leads.
Single Pole Multiple Throw (SPnT) Pull Chain Switch
The pull chain switch that controls the fan, is a single pole multiple throw switch. It has multiple positions, which allows it to control the speed of the fan. Draw simply, it would look something like this.
![enter image description here](https://i.stack.imgur.com/r2bCG.png)
Switch shown in OFF (Open) position.
When the chain is pulled and released on this switch, the internal contact rotates 45° (1/8 turn) to the next position.
![enter image description here](https://i.stack.imgur.com/3r5la.png)
Another pull, another turn.
![enter image description here](https://i.stack.imgur.com/rPFM6.png)
Pull again, turn some more.
![enter image description here](https://i.stack.imgur.com/XJ3Fv.png)
One final pull brings the switch 180° around, and again to the OFF (Open) position.
By manipulating the output of this switch, the fan is able to whirl around at various speeds depending on the switches position. The number of output leads, will depend on the switch. How those leads are connected to the fan motor, will depend on the fan manufacturer. This simply illustrates the basic principle of how the switch works.
As always electrical work can be dangerous, never be afraid to contact a qualified Electrician
The only way to know for sure, is to pull the fixture down and have a look at the wiring. If power comes from the panel to the fixture first, then this is trivial. If power goes to one of the switches first, then you're likely out of luck.
If you are lucky, and the power does go to the fixture first. Simply connect the black wire from the fan, directly to the ungrounded (hot) supply conductor. Leave the blue wire from the fan connected how it is.
As BrownRedHawk mentioned in a comment, installing a remote might suit your needs. Though you may want a remote at each switch location, which complicates the installation a bit.
Best Answer
Yes, it can be done easily by pigtailing wires inside the junction box under the light; one part is 'unswitched', wires coming from the source go into the box and split into two sub-branches; one goes through the box and continue on to the plugs, while the other half splits to branch off to the new wall switch, a "switch loop", and then back up to power the light.