Yes, of course.
Even if the foundation is with spf, the skin still tans, since no spf blocks 100% of the sun's rays. But when you are in the sun, it is better to always use foundation with spf in the composition.
Foundation consists of water, silicone base and pigment (powder). In a hot season, in a warm room, the pores expand, and all the pigment is clogged in them, provoking the appearance of comedones and acne. As a rule, any good foundation contains at least minimal sun protection. In basic formulations, it equals 5-10 units and in most cases is not even indicated on the packaging.
Any exposure to ultraviolet rays (whether direct sunlight or tanning in a tanning bed) negatively affects the skin of the face, therefore, sunbathe deliberately, without rinsing off the foundation is not recommended. As an example: in a foundation under the sun's rays, your skin feels the same as you jogging in a down jacket under the same rays. When it comes to an ordinary walk along a sunny street lasting less than 2-3 hours, then you don't have to worry about the skin: it is protected and will not burn. If you are worried about the aesthetic appearance of the skin, then get a powder with a high degree of protection against UV rays, similar to that in the brands Clinique and isClinical, and use sunscreens with a non-greasy texture so as not to provoke rashes on problem skin.