Yes. They belong to the same subgenus: Prunus amygdalous.
Genetic similarity is high between a peach and an almond and you can cross them.
There is a theory saying peaches and almonds have a common ancestor originating in Asia and these species separately evolved after lifting of Himalayas. 
Peaches originated in northwest China. Wild almonds originated in central and western Asia. Today peaches are native to northwest China and almonds are native to Iran.
Almonds and peaches trigger similar allergic reactions. Their allergic properties from Amygdaloideae subfamily (plum, cherry, apricot, peach, and almond) is also similar to Maloideae subfamily (apples and pears).