Personally, I don't believe I could.
Emotional intimacy and physical intimacy are both different parts of my interpersonal relationships. Some of the people I am closes to emotionally, I have no interest in physically.
However, I would be lying if I said physical intimacy is entirely unimportant to me. Those I find most attractive are those that I can be physically and emotionally intimate with (I will define each of those in a moment for clarification) in a long-term manner. It honestly wouldn't be fair to whomever my asexual partner would be to not be able to express both forms of intimacy to the full extent, as they are quite intertwined in a very specific way.
Emotional intimacy, to me, is the extent at which I can expose my thoughts and feelings without fear for backlash. Those that I am closest to emotionally are those I feel like I can trust to keep my feelings and private thoughts secret as well as those who feel they can trust me in the same way. Both are required for the utmost in emotional intimacy. With an asexual person, I feel that this is entirely possible and wouldn't mind reaching that point with someone.
Physical intimacy is the desire for physical contact, scaling from friendly hugs all the way to full-on sexual intercourse. To reach the extent of physical intimacy that I desire with my partner, we'd both have to want all forms of contact with each other along that scale. An asexual partner wouldn't want me back, no matter how much I wanted them, and that would constantly needle into my mind and make me feel selfish. Half of the enjoyment of sexual activity, at least for me, is the act of giving my partner pleasure by mutual fulfillment of desire.
One might wonder how these can tie in together. While I am engaging in sexual activity is the time I feel the most vulnerable. I cannot bring myself to have sex with someone I do not care about in a very significant way. I can cuddle and even kiss, but I cannot expose myself sexually. The full extent of that vulnerability happens when I let my partner take charge and initiate as well as directing how we do things, which is not something I can see happening when it comes to an asexual partner, even if they do allow sexual activity.
Very much so, I am one who likes to maintain control of a situation. I don't drink alcohol, I don't smoke, I don't do drugs because all of these things affect, in some way or another, my ability to maintain control over my mind and body.
Additionally, while in a relationship I cease to feel physical attraction to those that aren't my partner so that bars the whole idea of separation of sexual and romantic partners.
Honestly, it just wouldn't be fair to her to have to initiate on something that she has no initial desire to do (even if the actual act gives physical stimulation and pleasure) for her to see me when I'm feeling most vulnerable (which is definitely something I want my long-term partner to see) and it wouldn't be fair to me to constantly feel guilty for pressuring her into something that she has no desire to do, even if she feels good while it's actually happening.
It's not out of any particular need to have sex, but I want to feel like I can trust my partner to see me when I'm feeling most vulnerable and I just don't see an asexual partner being interested in the act that would have that happen.
For reference, I am a heteromantic, heterosexual (although slightly bi-curious), male.
