Can I put my Outlook pst data file in SkyDrive or Dropbox and use it as my active Outlook pst file so my two PCs can both sync and use the same pst file?
No, while you can place a copy of it there, so you’ll create an on-line copy too, it is not recommended to use it as your active pst-file.
Synching will corrupt your pst-file
Due to the active connection and lock Outlook has on the file, SkyDrive/Dropbox (or something similar like Google Drive) will continuously try to upload the file and thus use a lot of network bandwidth. It is very likely that this will end up in an incomplete or otherwise corrupted online copy which will sync to another device and/or back to you computer and result in a complete loss of the pst-file.
Even when you were to use SkyDrive/Dropbox as an intermediary to copy over the pst-file between multiple computers (replacing the older local pst-file in another location), this could still lead to mail profile corruption and rules not working.
If you really want to have 2 PCs in sync, it would be better to look at using an IMAP, Exchange/Office 365 or Hotmail account type instead of POP3.
To still achieve it with POP3, you’ll need to use a 3rd party add-in. Several are listed in the Quick Tip Sync via USB drive and also contains solutions for synching via the Internet or local network.
Note that you can also use a Hotmail account with your own current email address.
SkyDrive or Dropbox as a pst backup location
Theoretically, you could use your SkyDrive/Dropbox as an online backup location. You would then backup your pst-file to your SkyDrive/Dropbox folder and then have it automatically synch to the cloud storage.
However, depending on the size of your pst-file and the network limitations set by your ISP, on-line storage (SkyDrive, Dropbox or something similar) might not be the solution at all.
For instance, upload speeds are often up to a factor 8 slower than your download speed and the amount of data which you are allowed to download/upload could have an upper limit too. Uploading a 1GB pst-file could then take a long time and daily backups will probably make you reach your monthly upload/download quota quite quickly.
If you really want to have cloud-based backups of your mail, consider using a mail host which backups the mail for you such as Office 365 or ask your current mail provider about their backup and restore policies (how long back, how long a restore would take, how much it costs, etc…).