Definitely! Just because many ultralight travelers (myself included) end up using bivy sacks, tarps and/or sleeping bag covers doesn't mean that's the only way to travel ultralight. In addition to personal preference some have for a proper tent (which is perfectly fine), you can approach the problem from a "pounds per person sheltered" perspective. In general, a solo backpacker won't be able to beat a bivy or tarp/bag cover combinations for weight (and I prefer the convenience as well). Once you can start sharing the load, however, the numbers can change to make a tent start looking very reasonable. Again, if you shop carefully.
Believe it or not, if you're traveling in a group a carefully selected shared tent is not particularly heavier (per person sheltered) than a solo bivy/tarp setup. Using a single large (8'x10') Siltarp to share (and perhaps an additional bug bivy or similar for those who don't want to try sewing in their own bug screen), you're probably looking at around 1 lb per person for a total solution, including a body sized piece of Tyvek, guy lines and stakes, etc.
For two trekkers sharing shelter, a Mountain Hardwear Waypoint 2 (2-person 3-season) weighs in at around 3.1 lbs, or about 1.6 lbs per person sheltered. Add in the tyvek and you're looking at just under 2 lbs per person for the total shelter system. Pretty sweet! Certainly not a burden.
If your budget can handle it, you can go even further with your tent options. Black Diamond now offers a line of ultralight tents inspired by Bibler (long known for featherweight-yet-very-pricey tents). Check out this list of shelters for some additional ideas.
There is a hybrid option between tent and tarp as well. Some tents can be deployed in a "fastpack" mode, using only the poles, stakes, and rainfly for shelter. Lay down a your body-sized piece of Tyvek for groundsheet and you're in business. Sierra Designs and Marmot are the two manufacturers I know of who have actively boasted of such a feature. In the case of the Sierra Designs Clip Flashlight 3 (3-person, 3-season), the Fastpack option weighs in at around 3lbs 3ozs, or a little over 1lb per person sheltered. Quite favorable.
So no, you don't have to rule out a tent if you want to travel with an ultralight (even down to a sub-10 lb.) base load. It all depends on tent selection and your ability to adequately share the total load. And even if you're solo, it can still work out favorably! Let's use my current 9.5 lb. base load as an example.
Assume for my solo load I swapped my Bug Bivy and tarp system (about 1.25 lbs) for a "heavy" 2-person Black Diamond Lighthouse (3.2 lbs). For the luxury of solo living in a tent that size, I'd add an additional 2 lbs to my load. Despite having a 2-person tent all to myself, my base load would only go from 9.5 lbs to 11.5 lbs! Perhaps not acceptable for a purist, but I think most folks carrying a sub-12 lb. base load would get by just fine without sore shoulders or compressed spines. ;-) And I can't imagine any 3-season backpacker having a 87"x51" + 43" peak tent to themselves and not feeling a bit spoiled. Ultralight decadence!
Tents and ultralight trekking can mix well! I hope I've been able to show that even the solo ultralight backpacker can wallow in relative luxury while still carrying what most would consider an exceptionally light load. Not the lightest load possible perhaps, but as we know it's all about personal comfort and goals. More possibilities and tradeoffs for you to consider.