I am sorry, but your question is not clear (at least not to me).
[If we place a DTE for a particular SLA in BSM, will we be getting alerts related to that profile through BSM?]
Do you mean you define Downtime in BSM and in its actions you selected a specific SLA or did you define SLA Data Correction or did you define SLA Status Alert?
[The alerts will be configured in EUM Module of BSM. The SLAs are configured in SLM Module.]
I don't see where is the problem. EUM Alerts have their own logic and can trigger alerts, and SLA Alerts are something else with their own logic.
[So is it possible that, the alerts configured in EUM module will still be triggered after placing DTE for that particular profile in SLM Module for the DTE Period?]
Yes. EUM Alerts are configured separately and SLA Alerts and Downtime are configured also separately. You can have Downtime event that will exclude data from SLM as well as suppress alerts from EUM or just suppress alerts from EUM. The Downtime actions are increasing (meaning each action is all the above and more).
The answer is YES, the EUM Alerts will be triggered. The "SLA Data Correction" is relevant (and you can guess it from its name) only for SLM.
Downtime and SLA Data Correction are NOT the same. They may appear similar but they are not. Downtime is central configuration which can affect several applications (such as SH, SLM, OMi, reports, etc) whereas SLA DC are relevant for SLM only.
Another difference is that Downtime can be defined ONLY for future time period whereas SLA DC can be defined also on historic time period.