Does the boiling point of an aqueous solution depend on what the solute is? Consider a situation where we have two aqueous solutions which have the same concentration (e.g. 1 M), but the solute is different. For example, one is a solution of glucose, and the other is a solution of ethanol.

I am aware that dissolving something in water can lead to changes in boiling point (e.g. elevation). But would the boiling points of these two solutions be affected in the same manner, given that the concentration of the solute is the same? Or will the exact boiling point depend on the chemical species that is dissolved?
No, in water the two solutions will not have the same boiling point.  

Ethanol is a volatile liquid with boiling point lower than water, and lowers the boiling point.

Water forms an azeotrope with ethanol.  There are positive and negative azeotropes, so when two or more volatile liquids are dissolved, you cannot easily predict whether boiling point will decrease or increase. 

There can also be cases, like adding HCl to water, where as solute is added, first the boiling point increases to a maximum (108 °C around 20% HCl) above the boiling point of water, then decrease to below the boiling point of water (48 °C for 38% HCl).

Glucose is non-volatile and increases the boiling point of water.  The boiling-point elevation formula can be applied to non-volatile solutes in volatile solvent.