Please check my solar outlay for Lithium ion battery
Updated to use correct 150W panel sizes. 


  Given:
   - 350w 36 volt motor.
   - 36V battery
   - Three 150w 12V panels, each rated at 12v, wired in series
   - MPPT controller unit  
  
  Would this be sufficient voltage to charge the battery with?


The panels will charge your battery.
A more important issue is, how much charge will the panels deliver to the battery?

"12 Volt" panels are typically rated at ~= 17 to 18V Vmp.
The Voc is higher again.
3 x "12V" panel;s will deliver about 50 Volts Vmp loaded.

A nominal 36V LiIon battery has 10 x 3.6V mean voltage cells. in series (and perhaps multiple strings of these in paralllel.
Vmax per cell is ~= 4.2V  or 42V/string.
The 50 Volt Vmp panels will provide more than enough voltage to charge the battery and the MPPT converter will optimise the voltage. 

In full sun, optimally aligned and clean and not too hot  the panels will deliver
Power = P = 3 x 150 Watts  = 450 Watts.
Under typical arrangements you may get 2/3 of this into the battery - more with care, or say 2/3 x 450 = 300 Watts.
At a mean voltage of 36V that's about 8 A battery charging current. If using typical 18650 cells you'll need typically about 3 strings of say 3.3 Ah LiIon cells charging at 1C to handle that current.
Or a battery of at least 30 cells configured as 10S3P say. = 36V x 10 Ah = 360 Wh.
That's not a large battery by ebike standards and you will probably wish to add more parallel strings.  I'll assume a "reference" battery of double that capacity - 10S6P, 60 cells, 36V 20 Ah, 720 Wh.

The above 10S6P 20 Ah battery charging at 20A would take usefully under an hour to charge to about 75% capacity and then several hours total to finish the last 25% due to the current tailoring off in the CV part of the usual CCCV charging cycle.  

So you could charge one 10S6P battery above to ~~= 75% of capacity per SSH / Sunshine hour / daily equivalent hour of full sunshine. 

Depending where you are and season you could get about 0 hours/day (Alaska in winter), about 2 hours/day (not quite snowing places in winter) and 5 or 6 or almost 7 hours per day in summer. 

The site www.gaisma.com will give you SSH per day (shown as kWh/m^2) for most locations on earth.

Where are you located?
Here are [dozens of USA locations Gaisma knows about] (https://www.gaisma.com/en/dir/us-country.html). Each of thos paes lists dozens of sub locations. There will be one near enough you - IF you are in the US. Similarly for Europe.

Here is the page for Atlanta in Georgia USA as an example.
This image from that page shows SSH/day in kWh/m^2 for Atlanta, Georgia. 
The average daily average SSH by month is shown.
In December there is about 2 SSH/day and for 5 or 6 months over 5 SSH/day.
With a 3.5 kWh battery (rather good) ~= 5 x the above 720 Wh example, you could charge it to 75% capacity for 5 or 6 months of the year and about 30% capacity (still useful) on an AVERAGE mid winters day.  In winter a clean snow free (if you get it) panel optimally pointed would be wise.