Yes, you could hear, but it would be harder to localize sounds.
The "ear" from a biological perspective includes the inner ear which is all of course necessary for hearing.
The external part of the ear is called the pinna/pinnae (plural), and yes, you can hear without pinnae; that's essentially what you do when you use in-ear headphones since they project right into the auditory canal and don't use the pinnae at all.
However, the pinnae are important both for collecting sound (therefore increasing the amplitude) and for sound localization, because they both shape the volume of sounds depending on direction (you can localize continuous sound by turning your head back and forth) and have a vital contribution to the head related transfer function that is crucial for localizing sound in elevation.
Sound localization experiments that use in-ear headphones sometimes first record the head-related transfer function with a microphone in the ear to then apply this filter to sounds that are played. This varies somewhat from individual to individual and captures the unique shape and position of the pinnae.
Note that sound localization is not only important for knowing where sounds are coming from, it can also be important to identify and pay attention to auditory objects, especially in noise, like one person talking in a cocktail party.
Algazi, V. R., Duda, R. O., Duraiswami, R., Gumerov, N. A., & Tang, Z. (2002). Approximating the head-related transfer function using simple geometric models of the head and torso. The Journal of the Acoustical Society of America, 112(5), 2053-2064.
Batteau, D. W. (1967). The role of the pinna in human localization. Proc. R. Soc. Lond. B, 168(1011), 158-180.
Brungart, D. S., & Rabinowitz, W. M. (1999). Auditory localization of nearby sources. Head-related transfer functions. The Journal of the Acoustical Society of America, 106(3), 1465-1479.
Hofman, P. M., Van Riswick, J. G., & Van Opstal, A. J. (1998). Relearning sound localization with new ears. Nature neuroscience, 1(5), 417.
Wenzel, E. M., Arruda, M., Kistler, D. J., & Wightman, F. L. (1993). Localization using nonindividualized head‐related transfer functions. The Journal of the Acoustical Society of America, 94(1), 111-123.