Yes and No. GLM can be used when the range of the data is limited. You will often see it used on responses that are 0-100 (like % grades) and that is analogous to your 0-1 range.
However, the assumption of normality is violated and you need to use the Central Limit Theorem to make useful inferences. In practice, this means that the closer your outcomes are to the extreme points in the distribution, the larger your sample size needs to be.
"Large" is a relative term. It would be prudent to do some bootstrap validation of your model to make sure that the parameter estimates are stable.