Yes, IMIconnect's messaging API supports batching. You can send personalised messages to a maximum of 1000 destinations at once. 

For example here is an example of a bulk SMS request -

[{
        "deliverychannel": "sms",
        "channels": {
            "sms": {
                "text": "Hi John, Greetings from MNOP bank. "
            }
        },
        "destination": [{
            "msisdn": ["91900000009"]
        }]
    }, {
        "deliverychannel": "sms",
        "channels": {
            "sms": {
                "text": "Hi Mark, Greetings from MNOP bank. "
            }
        },
        "destination": [{
            "msisdn": ["91900000008"]
        }]
    }, {
        "deliverychannel": "sms",
        "channels": {
            "sms": {
                "text": "Hi steve, Greetings from MNOP bank. "
            }
        },
        "destination": [{
            "msisdn": ["91900000007"]
        }]
    }

]

And the corresponding response -

{
  "response": [
    {
      "description": "Queued",
      "correlationid": "",
      "code": "1001",
      "transid": "29e6cff5-5f0d-4872-b336-57799cb63da7"
    },
    {
      "description": "Queued",
      "correlationid": "",
      "code": "1001",
      "transid": "29e6cff5-5f0d-4872-b336-57799cb63da7_1"
    },
    {
      "description": "Queued",
      "correlationid": "",
      "code": "1001",
      "transid": "29e6cff5-5f0d-4872-b336-57799cb63da7_2"
    }
  ]
}
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