Can I supply the board's 3.3V directly to the AREF pin?
In Atmel's doc8271 pdf (with specification details for ATmega48A; ATmega48PA; ATmega88A; ATmega88PA; ATmega168A; ATmega168PA; ATmega328; and ATmega328P), table 29-20 on page 117 shows R_REF (the AREF input resistance) as 32KΩ (typical).  Section 24.5.2 on page 248 suggests that AREF is to be treated as a high-impedance input or output:


  ... the reference voltage can be made more immune to noise by connecting a capacitor between the
  AREF pin and ground. VREF can also be measured at the AREF pin with a high impedance voltmeter. Note that
  VREF is a high impedance source, and only a capacitive load should be connected in a system.


Also note that there is no reason to connect anything to AREF (pin 21), because on a standard Uno, AVCC (pin 20) is connected to VCC (pin 7), and one can select AVCC as the reference voltage during analog converter setup [as explained below].  Quoting again from section 24.5.2:


  VREF can be selected as either AVCC, internal 1.1V reference, or external AREF pin.  AVCC is connected to the ADC through a passive switch. The internal 1.1V reference is generated from the internal bandgap reference (VBG) through an internal amplifier. In either case, the external AREF pin is directly connected to the ADC...


Summary: you can connect the 3.3V pin and the analog reference pin (AREF) directly, but on a 3.3V system  there is no reason to do so.

Selecting AVCC as the reference voltage:  Say analogReference(DEFAULT) to select AVCC as the reference voltage.  According to arduino.cc, this will choose “the default analog reference of 5 volts (on 5V Arduino boards) or 3.3 volts (on 3.3V Arduino boards)”.