In the PHB on page 147 about reach weapons:
Reach. This weapon adds 5 feet to your reach when you attack with it, as well as when determining your reach for opportunity attacks with it.
In the PHB on page 237 about the Enlarge/Reduce spell:
Enlarge: The target’s size doubles in all dimensions, and its weight is multiplied by eight. This growth increases its size by one category—from Medium to Large, for example. If there isn’t enough room for the target to double its size, the creature or object attains the maximum possible size in the space available. Until the spell ends, the target also has advantage on Strength checks and Strength saving throws. The target’s weapons also grow to match its new size. While these weapons are enlarged, the target’s attacks with them deal 1d4 extra damage.
Even if it's not specifically stated in the rules and it might lead to making the spell that much powerful (especially with the Sentinel feat) I find it unreasonable to tell my players that an enlarged glaive doubles it's dimensions but not it's physical properties like reach.
Best Answer
No
Spells do only what they say they do - Enlarge increases the size by 1 category and increases the size of the weapon (doing more damage) but does not increase the reach of the weapon.
Remember that a creature enlarged from medium to large effectively increases reach by 5 feet (more or less) anyway since it now occupies 10 feet of space rather than 5. Small to medium enlargements do not get this.