Yes, you can have ActiveSync and BES at the same time. It should "just work". If not it may be firewall or the service is turned off. Check the FAQ here but your admin may have to research.

 

There are quite a bit of things in Exchange that can effect the Droid with syncing your email. There's a thread here where myself and a few others go through some issues.

Basically 1) make sure Outlook Web Access is working CORRECTLY. 2) If ActiveSync has device security enabled, you MUST disable it on a per user basis for the built in email on the Droid to access Exchange Email. 3) Make sure Outlook Mobile Access is enabled and to Enable Unsupported Devices, 4) for "Exchange Server" you must put the fully qualified domain name that you use to access webmail or also can be called a Front End server.

Anyways, with that said, take a look at that thread. Hopefully it'll help. I didn't have to use Touchdown and so far I've had no problems at all.

As for BES (Blackberry Enterprise Server), you can run them both at the same time. BES isn't cheap, ActiveSync is part of Exchange and is included free of charge.

Here's the thread I mentioned.
http://androidforums.com/motorola-droid/19273-i-took-my-droid-back.html

 

This might be relevant to you and many other android users. I got outlook 365 (outlook web app) to work on my samsung epic/galaxy phone.

The first field is misleading

DOMAIN: USER NAME
actually enter it like this...
emailsuffix.com\name@emailsuffix.com (whatever yours is)
EX: mindhead.onmicrosoft.com\tony@mindhead.onmicrosoft.com
or EX: mindhead.us\tony@mindhead.us (or whatever yours is)

PW: your password

EXCHANGE SERVER: NOT what is auto populated, not what is instructed by the outlook 365 portal website, not what is instructed by techrepublic, but this...
if you are logged into outlook 365 portal on the browser, look at the address field, in my case it was this...

XXXXXXXXXX.outlook.com

(I put Xs in place of characters, yours are probably unique, perhaps something like ch1prd0709)
Some people's phones might require something slightly different...but this is what was successful on the Samsung Epic/Galaxy phone.

It took me hours to figure this out because all of the information out there that was wrong, trying different combinations of the false information...but I was obsessed, so I did it.