Yes and no. The answer is kind of tricky to explain, but I'll do my best here...
Primers are basically silicone-based fluids, gels, or liquids that sit on top of the skin and create a smooth, even surface. There are plenty of skin care products out there that have the same basic cosmetic chemistry as a primer, but they're sold as serums or moisturizers. Typically primers are oil-free and can comfortably be called non-comedogenic. BUT...
Many, many people--myself included--have had severe breakouts from traditional makeup primers like Smashbox Photo Finish, which is a HG for a ton of people. The thing you have to take into consideration is that you're applying another layer of product to your skin. And if your skin was already treated with skin care products that contain thickeners and emollients, as well as being topped with makeup products that have even more emollients... Well... That can make breakouts a real issue.
A lot of people blame the silicones, which is somewhat baffling because silicones are basically in everything. If you can't use silicone, you can't use the majority of cosmetic products on the market and most medical supplies. However, if you are allergic to latex, you will be more likely to react to primers because the silicones they use in cosmetics can sometimes be contaminated with latex. This can create an allergy that can mimic breakouts.
Regardless of that...You need to think about whether or not you really need a primer before adding one, and you may want to see if any of your motives are coming from flaws in the routine you already have. If your skin care routine is not very efficient, then your makeup will definitely suffer. And if you're choosing the wrong foundation, concealer, and powder for your skin type, then it won't go on so well either.
If you find one that can multitask, you'll be pretty happy with a primer, and that means looking beyond the silicones. Finding one that includes SPF, anti-aging ingredients, salicylic acid, niacinamide, or brightening ingredients will really be beneficial to acne. And you can also find perfectly good primers that are being sold as serums, which contain hyaluronic acid, peptides, antioxidants, or AHAs. Color correctors will allow you to use less foundation, making product overload a non-issue. Finding out what you need and choosing a formula that is as lightweight and nonirritating as possible is critical to avoiding breakouts from primers--or anything you use.
If you choose to use a primer on a regular basis, it's important that you adjust your morning routine accordingly because you may need lighter products or find you can skip some of them all together. And you may even find that the products you were using before were the very reason your makeup wasn't very longwearing in the first place, making adding one more thing a tipping point for your skin.
It's also terrible for acne prone skin to experience a lot of friction, so prolonging your makeup application with more rubbing and blending can be too much for easily stimulated skin.
Silicones can turn real ugly if you don't cleanse your skin twice a day religiously. They are semi-occlusive and create a weightless film on the skin. They kind of form a "breathable web" that won't suffocate your skin like petrolatum or waxes, but they still create a protective barrier that can shield your skin from the environment and even comedogenic products that would otherwise break you out.
If you don't apply them to clean skin, you can drive any grime or bacteria deeper into your pores. So many people skip their morning cleanse, which is a huge, huge mistake. You have to remove the products you applied the night before and dead skin cells--not just dirt.
You also need to be sure you're removing them properly at night, which isn't an easy task for anyone using a cleanser or makeup remover that isn't designed to break down silicones. Because silicones feel weightless on the skin, you'll have no idea you didn't remove them either. You need to use either a dual-phase makeup remover (like Lancome Bifacil), a cleansing oil, or oil-containing makeup remover (like Clinique TTDO Cleansing Balm) followed by cleanser that contains cocoamidopropyl betaine (like Peter Thomas Roth Gentle Foaming Cleanser). Sulfates just don't break down silicones, and most toners don't either.
You also cannot sweat in them. Period.
Sorry for being longwinded... I hope this made sense. Acne prone skin is a real pain to keep in balance--with or without primers. When all else fails, patch test. =)