So any compound that binds the androgen receptor will exert negative feedback. The result of that feedback affects multiple systems. The most obvious effect is that total test will decrease slightly, as may lh and fsh depending on the dose. The other is that shbg will be decreased. That will increase the amount of free test relative to total test, such that your overall free test will likely not be affected, depending on dosing. However, a side effect of decreasing shbg is that your free estrogen will increase because it's not bound by shbg. Therefore, while ostarine won't aromatize or increase total e2, it will increase free e2.
Gtx wrote this in their abstract about ostarine when it was initially published: "In men, no statistically significant differences from placebo in change from baseline values for free testosterone, DHT, estradiol, follicle-stimulating hormone (FSH), or LH were observed at any GTx-024 dose. However, sex hormone-binding globulin (SHBG) was significantly reduced with GTx-024 3 mg versus placebo. The decrease in SHBG was accompanied by a reduction of serum total testosterone in subjects treated with 1 mg or 3 mg of GTx-024 compared to placebo. This data demonstrates that Ostarine is total testosterone suppressive but free testosterone, LH and FSH were not statistically suppressed."