No, my friend, an insulin pump does NOT work like that. Having said that, there IS a CGMS (Continuous Glucose Monitoring System) that can work alongside an insulin pump, and this CAN make your pump alarm if your blood sugar (glucose) level falls too low. It can also suspend your pump from delivering insulin. You are, though, jumping the gun a little. Pumps can be set up to deliver less insulin at different times of the day ... or night ... based on your insulin requirements at these times. (My pump has 7 different delivery settings (basal rates) throughout any 24 hour period, but these can be added to if the need is there.)
The CGMS is another fitting that you have to 'implant' into your body that communicates wirelessly with the pump, and these are very expensive. They also need to be changed every few days, just as the cannula, the 'implant' that delivers insulin, does.
You don't say whether these night-time hypos a regular occurrence, or whether there is, in fact, a pattern to them, but I'm quite sure that if you inform your doctor that you're having these night-time hypos that s/he will take this into account when directing you what basal rates you should be infusing.
I'm quite sure, my friend, that once you've got used to using a pump you'll wonder why it took you so long to make the transition. It's like getting a new lease of life ... especially for people who have difficulty in maintaining a stable blood sugar level.
I forgot to say that you need to be able to calculate the amount of carbohydrates that you imbibe (either eat or drink), and then direct the pump to infuse sufficient insulin to cover that amount. You WILL also need to wake up during the night to test your blood sugar levels as pumps only use fast-acting insulins, and there's a danger, if the basal rate(s) are set too high, that you could suffer hypos. (Don't worry about this, once you're satisfied that you're not getting the hypos during the night, you won't need to wake yourself up to test.)
Best of luck.