It probably won't. One lens on the camera, plus two more, is about it. (The 55mm might fit in one of the front pockets, but they are unpadded.)
There is one thing that goes in my favor. I always wear my Billingham photo vest in the field.
This past week in Iceland for example, I had the A7R2 on a BR strap with a lens attached - usually the Batis 25. Additionally, I had the Pentax 645z on another BR strap on one side, with the 45-85 lens on it (I was wearing the dual strap). Often this would be quite enough for a long hike and doing waterfalls. I had the RRS tripod with the Cube on top and had no problems overall.
I also had the following items in my vest.
Two additional lenses - usually the Batis 85 and the 16-35 f4
My iPhone 6+
Small Moleskine notebook and pen
Four A7R2 batteries and two Pentax batteries
Two additional SD cards
Giotto rocket blower, small microfiber cloth, lenspen
Smartwool balaclava (for when it got really windy)
Pair of Heatsmart gloves - unless I was wearing them
Singh-Ray 10 stop ND filter in its case
Lee 0.6 and 0.9 GND filters in a cloth pouch
Lee filter holder with 67mm and 72mm rings
Small Allen wrench
Sony lens back cap and camera cap in case I had to take the lens off the camera.
Packet of gum
Small ziploc bag with a few of my favorite teabags
Small rain cover in a pouch.
Believe it or not, the vest had room for more!
The only problem I had was it was not easy to take the lenses in and out of the vest pockets and I was afraid of dropping them especially when wearing gloves. Also, there was nowhere to put the camera if it started raining. In addition, I had to be very careful climbing in and out of the vehicle and negotiating the lava rocks in case I bumped the cameras against something.
So, at least for me, the Hadley Small may be quite adequate.