Yes and No
The fibreglass does the same job as oiling the bat i.e. retains the moisture content of the willow, but with the added bonus of adding some extra protection.
Personally, I would recommend changing the fibreglass sheet/tape once a year, but you can leave it on if you wish.
I change mine because there may be some damage underneath the fibreglass that you cannot see. When damage is treated early, it can save your bat.
Secondly, the fibre glass sheet/tape can cause delamination of the bats face if left on for too long.
If your not too worried about the bat and you don't want the trouble of taking the tape off, just give the exposed wood on the bat a quick rub down with sand paper and a light coat of oil. If however you do want to tackle taking the tape off, you can cut along the edge with a Sharpe knife then heat up the tape with a hairdryer for around 2-3 minutes (loosens the glue) and then gently peel it off.
I usually take mine off at the end of the season, give the bat a light sand and oil and then reapply a sheet at the start of the season.
*you will get a much better finish if you use a scuff sheet on the face instead of tape and just use the tape to reinforce the edges and toe
As with most things in cricket I'm sure other people will have their own theories and opinions.