Sort of but not really. Only a few Ukrainian units have received western training and the majority of the Ukrainian army lacks body armor and even trucks to move around. In fact the majority of the Ukrainian army are sitting around in their barracks doing little more then peeling potatoes for their supper, and some fairly primitive training. Even in the portion of the Ukrainian army actually at the front, there is a heavy deficit of trucks, and light armor vehicles. There is also a shortage of artillery. So far it's been compensated by bringing back retired types from the arsenal, but it can only go so far. Another big fight like Debal'tsevo or summer of '14, and the Ukrainian Army will no longer be able to fill the hole in artillery units. Finally, Ukraine has received some new light armor, but far too little, and the quality of what they've received leaves much to be desired. Remember those defective BTR-4s that the Iraqis turned down due to cracks in the armor? Those went to the Ukrainian Army and National Guard. And of course those rather garbage armored cars from Streit Group (and that's not my opinion, there are repeated reports from the Ukrainians that the Cougar and Spartan armored cars have huge mobility issues, break down frequently, and are uncomfortable and poorly designed for combat use). So while this stuff might look pretty at handover ceremonies, Ukraine would be lucky to get more up-armored Humvees.
That having been said, there's a few things they've done that are likely to matter quite a bit. They've got 3 squadrons of Su-25s flying now, with repairs done locally. That's quite a lot. And while Russian air defense is likely to be inside the combat zone again, 36 aircraft in a war this small means they can eat some casualties and still operate. They
have managed to scrape together enough artillery for the units currently at the front. Their use of artillery (just like the rebels) is very inefficient, reminiscent of WWII. But they've got enough, for now. For one more big fight anyway. They also have a core of experienced personnel who've fought in '14 and '15. While many of the conscripts de-mobbed, and many have even left the country (at least a couple making it as far as where I am in California), there is a core of officers and NCOs still around that have extensive combat experience.
Overall it's not the strength of the Ukrainian military I'd count on but the weakness of the rebels. They couldn't even close the Debal'tsevo pocket without having to involve Russian armor and SpN. It's likely they rebels can hold well enough on the defense, for a while anyway, but for any sort of maneuver war, or serious offensive action (even counter-offensive) they would need Russian units. Not volunteers embedded with them, actual units.
EDIT: An interesting photoset from Azov regiment. That "social-nationalist" unit that's now part of the MVD. Note the very pretty display, and fresh paint. Note also the tiny quantity of vehicles actually being shown. Azov regiment is a relatively effective fighting force, and has been the recipient of a larger proportion of vehicles and equipment then line Army units.
Техника полка ваффен-СС "Ðзов" "ÐГУ" Свидомии - nortwolf_sam
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