Can I perform a Logistic regression on this data?

Yes. If you have numeric features for a classification problem, you can apply logistic regression.

However, you are unlikely to see spectacular results for this data. Let's look at the classic example Iris data set that does perform well under logistic regression:

This data set works well because the classes are largely linearly separable. Essentially, you could draw lines on that graph to separate the classes. Logistic regression is able to learn this and correctly classify most samples.

In the case of your data, logistic regression (and all other methods of classification) will struggle in the "overlapping" region because the features you have available simply don't provide enough information to correctly identify classes in the this region. You should still see some success outside of this region.

The best way to answer whether or not logistic regression will meet your needs is to run an experiment. Run it on your training data while holding back a test set and check performance on the held out data. If this gives performance that meets your needs, you're good to go. Otherwise, you'll likely need to explore additional features or come up with another way to solve this problem.